789 results on '"Simple ring"'
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2. Functional identities and their applications.
- Author
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Brešar, Matej
- Subjects
HOMOMORPHISMS ,POLYNOMIALS ,QUOTIENT rings ,POISSON algebras ,MATHEMATICAL models - Abstract
This paper surveys the theory of functional identities and its applications. No prior knowledge of the theory is required to follow the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
3. On higher commutators of rings.
- Author
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Lee, Tsiu-Kwen
- Subjects
- *
COMMUTATION (Electricity) , *NONCOMMUTATIVE rings , *COMMUTATORS (Operator theory) - Abstract
For a subset T of a ring R we denote by ℐ (T) the ideal of R generated by T. Given a higher commutator L of R , if R = ℐ (L) then R = L + L 2 ? The question is motivated by the result that a ring R is equal to its subring generated by [ R , R ] if R is either a noncommutative simple ring (by Herstein) or a unital ring with 1 ∈ [ R , R ] (by Eroǧlu). In this note, we study the question for the rings R satisfying the property that every proper ideal of R is contained in a maximal ideal (in particular, if R is finitely generated as an ideal). [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
4. Rings with fine nilpotents.
- Author
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Călugăreanu, Grigore and Zhou, Yiqiang
- Abstract
A nonzero sum of a unit and a nilpotent element in a ring is called a fine element. This is a study of rings in which every nonzero nilpotent is fine, which we call NF rings. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
5. Simple Right-Symmetric (1, 1)-Superalgebras.
- Author
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Pozhidaev, A. P. and Shestakov, I. P.
- Subjects
- *
LIE superalgebras , *ALGEBRA - Abstract
It is proved that 2-torsion-free simple right-symmetric superrings having a nontrivial idempotent and satisfying a superidentity (x, y, z) + (−1)z(x+y)(z, x, y) + (−1)x(y+z)(y, z, x) = 0 are associative. As a consequence, every simple finitedimensional (1, 1)-superalgebra with semisimple even part over an algebraically closed field of characteristic 0 is associative. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
6. Maximal zero product subrings and inner ideals of simple rings.
- Author
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Baranov, Alexander and Fernández López, Antonio
- Subjects
- *
RING theory , *LIE algebras , *BIJECTIONS , *MANUFACTURED products , *ARTIN rings - Abstract
Let Q be a (not necessarily unital) simple ring or algebra. A nonempty subset S of Q is said to have zero product if S 2 = 0. We classify all maximal zero product subsets of Q by proving that the map R ↦ R ∩ LeftAnn (R) is a bijection from the set of all proper nonzero annihilator right ideals of Q onto the set of all maximal zero product subsets of Q. We also describe the relationship between the maximal zero product subsets of Q and the maximal inner ideals of its associated Lie algebra. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
7. Non-Unital Ore Extensions
- Author
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Lundström, Patrik, Öinert, Johan, Richter, Johan, Lundström, Patrik, Öinert, Johan, and Richter, Johan
- Abstract
We study Ore extensions of non-unital associative rings. We provide a characterization of simple non-unital differential polynomial rings R[x; delta], under the hy-pothesis that R is s-unital and ker(delta) contains a non-zero idempotent. This result gener-alizes a result by oinert, Richter and Silvestrov from the unital setting. We also present a family of examples of simple non-unital differential polynomial rings.
- Published
- 2023
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8. Finite Dimensional Division Algebras
- Author
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Brešar, Matej, Axler, Sheldon, Series editor, Capasso, Vincenzo, Series editor, Casacuberta, Carles, Series editor, Mcintyre, Angus, Series editor, Ribet, Kenneth, Series editor, Sabbah, Claude, Series editor, Süli, Endre, Series editor, Woyczynski, Wojbor A., Series editor, and Brešar, Matej
- Published
- 2014
- Full Text
- View/download PDF
9. Some results on skew Hurwitz series rings.
- Author
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Tehranchi, Abdolreza and Paykan, Kamal
- Abstract
A ring is quasi-Baer (respectively, Baer) in case the right annihilator of every ideal (respectively, subset) is generated by an idempotent, as a right ideal. In this article, we investigate on the relationship between the quasi-Baerness, Baerness, semiprimitivity, simplicity and NI properties of a ring R, and its skew Hurwitz series ring (H R , α) , where R is a ring equipped with an endomorphism α . [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
10. Simplicity of Ore monoid rings.
- Author
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Nystedt, Patrik, Öinert, Johan, and Richter, Johan
- Subjects
- *
MONOIDS , *DIFFERENTIAL dimension polynomials , *COMMUTATIVE algebra , *POLYNOMIAL rings , *FINITE fields - Abstract
Given a non-associative unital ring R , a monoid G and a set π of additive maps R → R , we introduce the Ore monoid ring R [ π ; G ] , and, in a special case, the differential monoid ring. We show that these structures generalize, in a natural way, not only the classical Ore extensions and differential polynomial rings, but also the constructions, introduced by Cojuhari, defined by so-called D -structures π. Moreover, for commutative monoids, we give necessary and sufficient conditions for differential monoid rings to be simple. We use this in a special case to obtain new and shorter proofs of classical simplicity results for differential polynomial rings in several variables previously obtained by Voskoglou and Malm by other means. We also give examples of new Ore-like structures defined by finite commutative monoids. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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11. A note on Lie ideals of prime rings.
- Author
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Lee, Tsiu-Kwen and Mozumder, Muzibur Rahman
- Subjects
- *
NOETHERIAN rings , *PRIME ideals - Abstract
In this paper, we characterize Lie ideals, which are either finitely generated ℤ -modules or maximal, in (centrally closed) prime rings. As consequences, we extend the results proved in [1] for finite dimensional central division algebras of characteristic not 2 to simple rings of arbitrary characteristic. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
12. Structure of rings with commutative factor rings for some ideals contained in their centers
- Author
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Hai-lan Jin, Nam Kyun Kim, Michał Ziembowski, Zhelin Piao, and Yang Lee
- Subjects
Statistics and Probability ,Matematik ,Pure mathematics ,Algebra and Number Theory ,Mathematics::Commutative Algebra ,Structure (category theory) ,Factor (chord) ,Simple ring ,CIFC ring,nilradical,center,strongly bounded ring,right quasi-duo ring,FC ring,simple ring,non-prime FC ring ,Center (algebra and category theory) ,Geometry and Topology ,Commutative property ,Mathematics ,Analysis - Abstract
This article concerns commutative factor rings for ideals contained in the center. A ring $R$ is called CIFC if $R/I$ is commutative for some proper ideal $I$ of $R$ with $I\subseteq Z(R)$, where $Z(R)$ is the center of $R$. We prove that (i) for a CIFC ring $R$, $W(R)$ contains all nilpotent elements in $R$ (hence Köthe's conjecture holds for $R$) and $R/W(R)$ is a commutative reduced ring; (ii) $R$ is strongly bounded if $R/N_*(R)$ is commutative and $0\neq N_*(R)\subseteq Z(R)$, where $W(R)$ (resp., $N_*(R)$) is the Wedderburn (resp., prime) radical of $R$. We provide plenty of interesting examples that answer the questions raised in relation to the condition that $R/I$ is commutative and $I\subseteq Z(R)$. In addition, we study the structure of rings whose factor rings modulo nonzero proper ideals are commutative; such rings are called FC. We prove that if a non-prime FC ring is noncommutative then it is subdirectly irreducible.
- Published
- 2021
13. Managing Network Partitions in Structured P2P Networks
- Author
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Shafaat, Tallat M., Ghodsi, Ali, Haridi, Seif, Shen, Xuemin, editor, Yu, Heather, editor, Buford, John, editor, and Akon, Mursalin, editor
- Published
- 2010
- Full Text
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14. A Dichotomy for the Gelfand-Kirillov Dimensions of Simple Modules over Simple Differential Rings.
- Author
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Gupta, Ashish and Sarkar, Arnab Dey
- Abstract
The Gelfand-Kirillov dimension has gained importance since its introduction as a tool in the study of non-commutative infinite dimensional algebras and their modules. In this paper we show a dichotomy for the Gelfand-Kirillov dimension of simple modules over certain simple rings of differential operators. We thus answer a question of J. C. McConnell in Representations of solvable Lie algebras V. On the Gelfand-Kirillov dimension of simple modules. McConnell (J. Algebra 76(2), 489-493, 1982) concerning this dimension for a class of algebras that arise as simple homomorphic images of solvable lie algebras. We also determine the Gelfand-Kirillov dimension of an induced module. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
15. Coordinate Assignment for Cyclic Level Graphs
- Author
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Bachmaier, Christian, Brandenburg, Franz J., Brunner, Wolfgang, Fülöp, Raymund, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, and Ngo, Hung Q., editor
- Published
- 2009
- Full Text
- View/download PDF
16. Decay of Invincible Clusters of Cooperators in the Evolutionary Prisoner’s Dilemma Game
- Author
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Chan, Ching King, Szeto, Kwok Yip, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Giacobini, Mario, editor, Brabazon, Anthony, editor, Cagnoni, Stefano, editor, Di Caro, Gianni A., editor, Ekárt, Anikó, editor, Esparcia-Alcázar, Anna Isabel, editor, Farooq, Muddassar, editor, Fink, Andreas, editor, and Machado, Penousal, editor
- Published
- 2009
- Full Text
- View/download PDF
17. Wedderburn-Artin Theory
- Author
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Lam, T. Y. and Lam, T. Y.
- Published
- 2001
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18. Applications of Normal Forms for Weighted Leavitt Path Algebras: Simple Rings and Domains.
- Author
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Hazrat, Roozbeh and Preusser, Raimund
- Abstract
Weighted Leavitt path algebras (wLpas) are a generalisation of Leavitt path algebras (with graphs of weight 1) and cover the algebras L ( n, n + k) constructed by Leavitt. Using Bergman's diamond lemma, we give normal forms for elements of a weighted Leavitt path algebra. This allows us to produce a basis for a wLpa. Using the normal form we classify the wLpas which are domains, simple and graded simple rings. For a large class of weighted Leavitt path algebras we establish a local valuation and as a consequence we prove that these algebras are prime, semiprimitive and nonsingular but contrary to Leavitt path algebras, they are not graded von Neumann regular. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
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19. Isomorphism between Endomorphism Rings of Modules over A Semisimple Ring
- Author
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Hery Susanto, Indriati Nurul Hidayah, Santi Irawati, and Irawati
- Subjects
Ring (mathematics) ,Pure mathematics ,Endomorphism ,Mathematics::Commutative Algebra ,Simple (abstract algebra) ,Semisimple module ,Simple ring ,Mathematics::Rings and Algebras ,Division ring ,Artinian ring ,Isomorphism ,Mathematics - Abstract
Our question is what ring R which all modules over R are determined, up to isomorphism, by their endomorphism rings? Examples of this ring are division ring and simple Artinian ring. Any semi simple ring does not satisfy this property. We construct a semi simple ring R but R is not a simple Artinian ring which all modules over R are determined, up to isomorphism, by their endomorphism rings.
- Published
- 2020
20. On differential polynomial rings over nil algebras
- Author
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Wen-Fong Ke and Mikhail A. Chebotar
- Subjects
Ring (mathematics) ,Pure mathematics ,General Mathematics ,Unital ,Simple ring ,Derivation ,Algebra over a field ,Mathematics ,Differential polynomial - Abstract
Let R be a nil algebra over a field of characteristic 0, and let δ be a derivation of R. Then the differential polynomial ring R[X,δ] cannot be mapped onto a unital simple ring homomorphically.
- Published
- 2020
21. Some salient feature of topological simple ring
- Author
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K Alli, U. Jerseena, and S. Syed Ali Fathima
- Subjects
Feature (computer vision) ,Computer science ,Salient ,Simple ring ,Topology - Published
- 2020
22. Laplacian Controllability of a Class of Non-Simple Ring Graphs
- Author
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Ping-Yen Yang and Shun-Pin Hsu
- Subjects
Discrete mathematics ,0209 industrial biotechnology ,Ring (mathematics) ,020208 electrical & electronic engineering ,02 engineering and technology ,Mathematics::Spectral Theory ,Connection (mathematics) ,Weighting ,Controllability ,020901 industrial engineering & automation ,Control and Systems Engineering ,Simple ring ,0202 electrical engineering, electronic engineering, information engineering ,Node (circuits) ,Adjacency matrix ,Laplace operator ,MathematicsofComputing_DISCRETEMATHEMATICS ,Mathematics - Abstract
The Laplacian controllability of a family of graphs that are non-simple is studied in the paper. Without the regular assumption that the adjacency matrix is binary, the authors consider more flexible weighting parameters to represent the practical connection strength between nodes. Suppose the node states of the graphs evolve according to the Laplacian dynamics. The Laplacian eigenspaces of a class of ring graphs are explored, by which a sufficient condition to render the graphs controllable with the minimum number of input is proposed. Numerical examples are provided to illustrate the theoretical results.
- Published
- 2020
23. Simplicity of Leavitt path algebras via graded ring theory
- Author
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Johan Öinert and Patrik Nystedt
- Subjects
16S88, 16W50 ,Rings and Algebras (math.RA) ,General Mathematics ,Mathematics - Operator Algebras ,FOS: Mathematics ,Mathematics - Rings and Algebras ,Leavitt path algebra ,Operator Algebras (math.OA) ,Algebra and Logic ,graded ring ,simple ring ,centre ,Algebra och logik - Abstract
Suppose that $R$ is an associative unital ring and that $E=(E^0,E^1,r,s)$ is a directed graph. Utilizing results from graded ring theory we show, that the associated Leavitt path algebra $L_R(E)$ is simple if and only if $R$ is simple, $E^0$ has no nontrivial hereditary and saturated subset, and every cycle in $E$ has an exit. We also give a complete description of the center of a simple Leavitt path algebra., Comment: 10 pages. From v1 to v2: Added references and updated Section 1
- Published
- 2022
- Full Text
- View/download PDF
24. Maximal zero product subrings and inner ideals of simple rings
- Author
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A.A. Baranov and Antonio Fernández López
- Subjects
Algebra and Number Theory ,010102 general mathematics ,Zero (complex analysis) ,01 natural sciences ,Combinatorics ,Set (abstract data type) ,Annihilator ,Simple (abstract algebra) ,Product (mathematics) ,Simple ring ,0103 physical sciences ,Lie algebra ,Bijection ,010307 mathematical physics ,0101 mathematics ,Mathematics - Abstract
Let Q be a (not necessarily unital) simple ring or algebra. A nonempty subset S of Q is said to have zero product if S 2 = 0 . We classify all maximal zero product subsets of Q by proving that the map R ↦ R ∩ LeftAnn ( R ) is a bijection from the set of all proper nonzero annihilator right ideals of Q onto the set of all maximal zero product subsets of Q. We also describe the relationship between the maximal zero product subsets of Q and the maximal inner ideals of its associated Lie algebra.
- Published
- 2019
25. Z-GRADED SIMPLE RINGS.
- Author
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BELL, J. and ROGALSKI, D.
- Subjects
- *
WEYL groups , *WEYL space , *GEOMETRY , *INTEGERS , *MATHEMATICS - Abstract
The Weyl algebra over a field k of characteristic 0 is a simple ring of Gelfand-Kirillov dimension 2, which has a grading by the group of integers. We classify all Z-graded simple rings of GK-dimension 2 and show that they are graded Morita equivalent to generalized Weyl algebras as defined by Bavula. More generally, we study Z-graded simple rings A of any dimension which have a graded quotient ring of the form K[t, t-1; σ] for a field K. Under some further hypotheses, we classify all such A in terms of a new construction of simple rings which we introduce in this paper. In the important special case that GKdimA = tr. deg(K/k) + 1, we show that K and σ must be of a very special form. The new simple rings we define should warrant further study from the perspective of noncommutative geometry. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
26. Wedderburn-Artin Theory
- Author
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Lam, T. Y. and Lam, T. Y.
- Published
- 1991
- Full Text
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27. Inter-layer synchronization of periodic solutions in two coupled rings with time delay
- Author
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Xu Xu, Dongyuan Yu, and Zaihua Wang
- Subjects
Divide and conquer algorithms ,Computer science ,Statistical and Nonlinear Physics ,Condensed Matter Physics ,Topology ,01 natural sciences ,Stability (probability) ,Synchronization ,010305 fluids & plasmas ,Matrix (mathematics) ,Coupling (physics) ,Simple ring ,0103 physical sciences ,010306 general physics ,Eigenvalues and eigenvectors ,Center manifold - Abstract
A coupled two-ring-network with time delay is developed to avoid the weakness of a simple ring topology. The divide and conquer algorithm is used to analyze the distribution of the eigenvalues of the adjacent matrix. The stability of the equilibrium and inter-layer synchronization of the periodic dynamics are studied, and the dynamical interactions between coupled rings which lead to complicated mirror and reflection waves are further analyzed. Special attention is paid on the generalized synchronization between two rings when the adjacent matrix has repeated eigenvalues. Numerical simulations verify the theoretical results, and show that the appropriate settings of the time delay and transverse coupling can guarantee the “backup and recovery” procedure.
- Published
- 2019
28. On higher commutators of rings
- Author
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Tsiu-Kwen Lee
- Subjects
Pure mathematics ,Ring (mathematics) ,Algebra and Number Theory ,Mathematics::Commutative Algebra ,Computer Science::Information Retrieval ,Applied Mathematics ,Astrophysics::Instrumentation and Methods for Astrophysics ,Commutator (electric) ,Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) ,law.invention ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,law ,Simple ring ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Computer Science::General Literature ,Maximal ideal ,Ideal (ring theory) ,ComputingMilieux_MISCELLANEOUS ,Mathematics - Abstract
For a subset [Formula: see text] of a ring [Formula: see text] we denote by [Formula: see text] the ideal of [Formula: see text] generated by [Formula: see text]. Given a higher commutator [Formula: see text] of [Formula: see text], if [Formula: see text] then [Formula: see text]? The question is motivated by the result that a ring [Formula: see text] is equal to its subring generated by [Formula: see text] if [Formula: see text] is either a noncommutative simple ring (by Herstein) or a unital ring with [Formula: see text] (by Eroǧlu). In this note, we study the question for the rings [Formula: see text] satisfying the property that every proper ideal of [Formula: see text] is contained in a maximal ideal (in particular, if [Formula: see text] is finitely generated as an ideal).
- Published
- 2021
29. Perfect rings for which the converse of Schur's lemma holds
- Author
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M. Alaoui and Abdelfattah Haily
- Subjects
Pure mathematics ,Noncommutative ring ,Primitive ring ,Mathematics::Commutative Algebra ,General Mathematics ,Semisimple module ,Simple ring ,Schur's lemma ,Division ring ,Artinian ring ,Simple module ,Mathematics - Abstract
If $M$ is a simple module over a ring $R$ then, by the Schur's lemma, the endomorphism ring of $M$ is a division ring. However, the converse of this result does not hold in general, even when $R$ is artinian. In this short note, we consider perfect rings for which the converse assertion is true, and we show that these rings are exactly the primary decomposable ones.
- Published
- 2021
30. Ring Laser for Angle Measurement Devices
- Author
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Olena Bezvesilna, Irina Cherepanska, Artem Sazonov, Petro Melnychuk, and Valerii Kyrylovych
- Subjects
Accuracy and precision ,Materials science ,business.industry ,Rotational speed ,Ring laser ,Ring (chemistry) ,Laser ,law.invention ,Optics ,law ,Simple ring ,Measuring instrument ,business ,Earth's rotation - Abstract
Angle measurement means are one of the advanced directions for the application of gas ring lasers. The requirements of ring lasers used in angle measurement devices are different, in many respects, from those used in navigation. A simple ring laser developed for implementation in high-precision angle measurement instruments is described. The main specifications are presented. Theoretical and experimental studies and computer simulation of ring laser parameters are presented. The studies were carried out, taking into account changes in the Earth’s rotation speed around the axis and without taking into account changes in the Earth’s rotation speed. The obtained results indicate that the change in the speed of rotation of the Earth affects the accuracy of a ring laser. In order to reduce this error, it is necessary to fulfill the requirements of the rotational axis of the ring laser relative to the rotational axis of the Earth. Methods of the accelerated tests are imperfect for determining a term of storage. Therefore, tests during a real storage term remain the most reliable. The operation of the ring lasers in angle measuring instruments for more than 20 years has demonstrated their high stability. Using the ring laser, the angle measurement means of accuracy that exceeds the accuracy of the existing National Standards for a plane angle can be developed.
- Published
- 2021
31. Note on some ideals of associative rings.
- Author
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Filipowicz, M. and Kȩpczyk, M.
- Subjects
- *
ASSOCIATIVE rings , *IDEALS (Algebra) , *MULTIPLY transitive groups , *MATHEMATICAL statistics , *SET theory , *MATHEMATICAL notation , *MATRICES (Mathematics) - Abstract
It is well known that being an ideal (left ideal, right ideal) of a ring is not a transitive relation. Nevertheless in some cases the transitive property does hold. Systematic studies of this subject were started in [11,13]. In this paper we continue these studies. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
32. Delays induced cluster synchronization in chaotic networks
- Author
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Marco Storace, Francesco Sorrentino, Ke Huang, Matteo Lodi, and Chad Nathe
- Subjects
Computer science ,Applied Mathematics ,Chaotic ,General Physics and Astronomy ,Statistical and Nonlinear Physics ,Topology ,Network topology ,01 natural sciences ,Stability (probability) ,010305 fluids & plasmas ,Coupling (computer programming) ,Simple ring ,0103 physical sciences ,Synchronization (computer science) ,Cluster (physics) ,Colpitts oscillator ,010306 general physics ,Mathematical Physics - Abstract
We study networks of coupled oscillators and analyze the role of coupling delays in determining the emergence of cluster synchronization. Given a network topology and a particular arrangement of the coupling delays over the network connections, different patterns of cluster synchronization may emerge. We focus on a simple ring network of six bidirectionally coupled identical oscillators, for which with two different values of the delays, a total of eight cluster synchronization patterns may emerge, depending on the assignment of the delays to the ring connections. We analyze stability of each of the patterns and find that for large enough coupling strength and specific values of the delays, they can all be stabilized. We construct an experimental ring of six bidirectionally coupled Colpitts oscillators, with delayed connections obtained by coupling the oscillators via RF cables of appropriate length. We find that experimental observations of cluster synchronization are in essential agreement with theoretical predictions. We also verify our theory in a fully connected network of fifty nodes for which connections are randomly assigned to be either undelayed or delayed with a given probability.
- Published
- 2020
33. Implementation of the toroidal absorption cell with multi-layer patterns by a single ring surface
- Author
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Chuanliang Li, Ruifeng Kan, Hong Chang, Xuanbing Qiu, Xiaohu He, Shiling Feng, Huiyan Meng, Weiguang Ma, Christa Fittschen, Qiusheng He, Xiaohua Yang, Guqing Guo, Taiyuan University of Technology, Nantong University, Institute of Laser Spectroscopy, Shanxi University, Physicochimie des Processus de Combustion et de l’Atmosphère - UMR 8522 (PC2A), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Shanxi University (SXU), Université de Lille, CNRS, 463444|||Taiyuan University of Technology, State Key Laboratory of Quantum Optics and Quantum Optics devices, and Physicochimie des Processus de Combustion et de l’Atmosphère - UMR 8522 [PC2A]
- Subjects
Physics ,Surface (mathematics) ,[PHYS.PHYS.PHYS-OPTICS]Physics [physics]/Physics [physics]/Optics [physics.optics] ,Toroid ,Stray light ,business.industry ,02 engineering and technology ,Radius ,021001 nanoscience & nanotechnology ,01 natural sciences ,Atomic and Molecular Physics, and Optics ,010309 optics ,Optics ,Path length ,Simple ring ,0103 physical sciences ,Ray tracing (graphics) ,[PHYS.PHYS.PHYS-INS-DET]Physics [physics]/Physics [physics]/Instrumentation and Detectors [physics.ins-det] ,0210 nano-technology ,business ,Optical path length - Abstract
International audience; We developed a type of toroidal multi-pass cell with multi-layer patterns based on the off-axis model. The effective path length of the original toroidal multi-pass cell is extended several roundtrips in comparison with the single-layer pattern, since the inner surface of the toroidal multi-pass cell is more efficiently utilized. The light pattern has been achieved by using the simple ring surface, which is easy to fabricate. The exact analytical equations for the design of the toroidal multi-pass cell were derived based on analytical vector calculations. A series of numerical ray tracing simulations is presented, and the maximum theoretical optical path length that can be reached is 30 m with a setup of 5 cm column radius. Furthermore, two practical spot patterns are demonstrated with a path length of 8.3 m for a two-layer pattern and 10 m for a three-layer pattern, with respective effective volumes of 63 mL and 94 mL. Furthermore, the fringe effect is substantially reduced to less than 0.5% by the usage of our designed mask.
- Published
- 2020
34. NOTES ON LIE IDEALS OF SIMPLE ARTINIAN RINGS.
- Author
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ARIANNEJAD, M. and EMAMI, M.
- Subjects
- *
LIE algebras , *ARTIN rings , *MATHEMATICAL proofs , *ASSOCIATIVE rings , *MULTIPLICATION , *REPRESENTATIONS of algebras , *MATHEMATICAL notation - Abstract
Let R be a ring. If we replace the original associative product of R with their canonic Lie product, or [a, b] = ab - ba for every a, b in R, then R would be a Lie ring. With this new product the additive commutator subgroup of R or [R, R] is a Lie subring of R. Herstein has shown that in a simple ring R with characteristic unequal to 2, any Lie ideal of R either is contained in Z(R), the center of R or contains [R, R]. He also showed that in this situation the Lie ring [R, R]/Z[R, R] is simple. We give an alternative matrix proof of these results for the special case of simple artinian rings and show that in this case the characteristic condition can be more restricted. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
35. Green's Relations in Rings and Completely Simple Rings
- Author
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Florion Cela
- Subjects
Combinatorics ,Mathematics::Commutative Algebra ,Simple (abstract algebra) ,Simple ring ,Structure (category theory) ,Zero (complex analysis) ,Division ring ,Green's relations ,Ideal (ring theory) ,Mathematics - Abstract
In this paper we prove that which of Green's relations $\mathcal{L,R,H}$ and $\mathcal{D}$ in rings preserve the minimality of quasi-ideal. By this it is possible to show the structure of the classes generated by the above relations which have a minimal quasi ideal. For the completely simple rings we show that they are generated by the union of zero with a $\mathcal{D} $-class. Also we emphasize that a completely simple ring coincides with the union of zero with a $\mathcal{D} $-class if and only if it is a division ring.
- Published
- 2018
36. The Curious Case of a Parasitic Twin of the Corroles
- Author
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Biju Basumatary, Rahul, R. V. Ramana Reddy, and Jeyaraman Sankar
- Subjects
Parasitic twin ,Materials science ,010405 organic chemistry ,General Medicine ,General Chemistry ,010402 general chemistry ,medicine.disease ,01 natural sciences ,Catalysis ,0104 chemical sciences ,Crystallography ,chemistry.chemical_compound ,chemistry ,Simple ring ,medicine ,Molecule ,Corrole ,Ring current - Abstract
An expanded porphyrinoid has been obtained by a simple ring expansion from a contracted porphyrinoid, namely corrole. Spectroscopic, structural, and computational investigations reveal peculiar π-conjugation and geometry. The effect of extended π-conjugation is evident from perturbed redox behavior and photophysical properties. Owing to the strong diatropic ring current of the corrole and cross-conjugation, the molecule exhibits a non-aromatic nature for the expanded π-circuit, as evident from NMR studies.
- Published
- 2018
37. Commuting traces of multilinear maps on invertible elements
- Author
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Willian Franca
- Subjects
Multilinear map ,Pure mathematics ,Algebra and Number Theory ,Unital ,010102 general mathematics ,010103 numerical & computational mathematics ,01 natural sciences ,law.invention ,Invertible matrix ,law ,Simple ring ,0101 mathematics ,Unit (ring theory) ,Mathematics - Abstract
Let R be a unital simple ring. Under some technical restrictions, we characterize m-linear mappings G:Rm→R satisfying [G(u,…,u),u] = 0 for all unit u∈R.
- Published
- 2018
38. One-pot heterocyclic ring closure of 1,1′-bi-2-naphthol to 7H-dibenzo[c,g]carbazole
- Author
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Fathy Hassan, Daisuke Hashizume, Masuki Kawamoto, Yoshihiro Ito, Takuji Hirose, and Krishnachary Salikolimi
- Subjects
Organic electronics ,010405 organic chemistry ,Carbazole ,1,1'-Bi-2-naphthol ,Organic Chemistry ,dBc ,010402 general chemistry ,Ring (chemistry) ,01 natural sciences ,Biochemistry ,0104 chemical sciences ,Amorphous solid ,chemistry.chemical_compound ,chemistry ,Simple ring ,Drug Discovery ,Polymer chemistry - Abstract
An operationally simple ring closure of racemic 1,1′-bi-2-naphthol (BINOL) yielded the heterocyclic aromatic compound 7H-dibenzo[c,g]carbazole (DBC). This one-pot method gave a good conversion and is suitable for gram-scale synthesis. DBC derivatives have high thermal durability, amorphous and crystalline structures with unique morphological properties, and semi-conducting behavior with potential applications in organic electronics.
- Published
- 2018
39. Note on Ideal Based Zero-Divisor Graph of a Commutative Ring
- Author
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K. Selvakumar, A. Mallika, and R. Kala
- Subjects
Principal ideal ring ,Reduced ring ,Discrete mathematics ,zero-divisor graph ,Algebra and Number Theory ,13a15 ,Applied Mathematics ,Commutative ring ,ideal based zero divisor graph ,clique number ,Combinatorics ,Primary ideal ,Principal ideal ,chromatic number ,05c69 ,Simple ring ,Radical of an ideal ,QA1-939 ,05c45 ,Zero divisor ,Mathematics - Abstract
In this paper, we consider the ideal based zero divisor graph ΓI(R) of a commutative ring R. We discuss some graph theoretical properties of ΓI(R) in relation with zero divisor graph. We also relate certain parameters like vertex chromatic number, maximum degree and minimum degree for the graph ΓI(R) with that of Γ(R/I ). Further we determine a necessary and sufficient condition for the graph to be Eulerian and regular.
- Published
- 2017
40. On polynomial rings over nil rings in several variables and the central closure of prime nil rings
- Author
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Edmund Puczyłowski, Mikhail A. Chebotar, Pjek-Hwee Lee, and Wen-Fong Ke
- Subjects
Ring (mathematics) ,Mathematics::Commutative Algebra ,General Mathematics ,Polynomial ring ,010102 general mathematics ,0211 other engineering and technologies ,Closure (topology) ,021107 urban & regional planning ,Mathematics - Rings and Algebras ,02 engineering and technology ,01 natural sciences ,Prime (order theory) ,Combinatorics ,Identity (mathematics) ,Rings and Algebras (math.RA) ,Simple ring ,FOS: Mathematics ,0101 mathematics ,Algebra over a field ,Mathematics - Abstract
We prove that the ring of polynomials in several commuting indeterminates over a nil ring cannot be homomorphically mapped onto a ring with identity, i.e. it is Brown-McCoy radical. It answers a question posed by Puczylowski and Smoktunowicz. We also show that the central closure of a prime nil ring cannot be a simple ring with identity, solving a problem due to Beidar.
- Published
- 2017
41. On finiteness of rings with finite maximal subrings
- Author
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H. E. Bell and A. A. Klein
- Subjects
PI-ring ,maximal subring ,prime ring ,simple ring ,radical. ,Mathematics ,QA1-939 - Abstract
It is conjectured that every ring with a finite maximal subring is finite. We prove this conjecture for PI-rings.
- Published
- 1993
- Full Text
- View/download PDF
42. Simple ambiskew polynomial rings.
- Author
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Jordan, David A. and Wells, Imogen E.
- Subjects
- *
POLYNOMIAL rings , *SET theory , *ITERATIVE methods (Mathematics) , *GENERALIZATION , *RING theory , *MATHEMATICAL analysis - Abstract
Abstract: We determine simplicity criteria in characteristics 0 and p for a ubiquitous class of iterated skew polynomial rings in two indeterminates over a base ring. One obstruction to simplicity is the possible existence of a canonical normal element z. In the case where this element exists we give simplicity criteria for the rings obtained by inverting z and the rings obtained by factoring out the ideal generated by z. The results are illustrated by numerous examples including higher quantized Weyl algebras and generalizations of some low-dimensional symplectic reflection algebras. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
43. Simplicity and maximal commutative subalgebras of twisted generalized Weyl algebras
- Author
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Hartwig, J.T. and Öinert, J.
- Subjects
- *
MAXIMAL functions , *COMMUTATIVE algebra , *WEYL'S problem , *PROOF theory , *INTERSECTION theory , *RING theory - Abstract
Abstract: In this paper we prove three theorems about twisted generalized Weyl algebras (TGWAs). First, we show that each non-zero ideal of a TGWA has non-zero intersection with the centralizer of the distinguished subalgebra R. This is analogous to earlier results known to hold for crystalline graded rings. Second, we give necessary and sufficient conditions for the centralizer of R to be commutative (hence maximal commutative), generalizing a result by V. Mazorchuk and L. Turowska. And third, we generalize results by D.A. Jordan and V. Bavula on generalized Weyl algebras by giving necessary and sufficient conditions for certain TGWAs to be simple, in the case when R is commutative. We illustrate our theorems by considering some special classes of TGWAs and providing concrete examples. We also discuss how simplicity of a TGWA is related to the maximal commutativity of R and the (non-)existence of non-trivial -invariant ideals of R. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
44. Multiparameter twisted Weyl algebras
- Author
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Futorny, Vyacheslav and Hartwig, Jonas T.
- Subjects
- *
WEYL groups , *ISOMORPHISM (Mathematics) , *GENERALIZATION , *MODULES (Algebra) , *LOCALIZATION theory , *MATHEMATICAL analysis - Abstract
Abstract: We introduce a new family of twisted generalized Weyl algebras, called multiparameter twisted Weyl algebras, for which we parametrize all simple quotients of a certain kind. Both Jordanʼs simple localization of the multiparameter quantized Weyl algebra and Hayashiʼs q-analog of the Weyl algebra are special cases of this construction. We classify all simple weight modules over any multiparameter twisted Weyl algebra. Extending results by Benkart and Ondrus, we also describe all Whittaker pairs up to isomorphism over a class of twisted generalized Weyl algebras which includes the multiparameter twisted Weyl algebras. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
45. Prüfer conditions in the Nagata ring and the Serre’s conjecture ring
- Author
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M. Jarrar and Salah-Eddine Kabbaj
- Subjects
Principal ideal ring ,Reduced ring ,Ring (mathematics) ,Algebra and Number Theory ,Mathematics::Commutative Algebra ,Mathematics::Number Theory ,Polynomial ring ,010102 general mathematics ,010103 numerical & computational mathematics ,01 natural sciences ,Nagata ring ,Algebra ,Combinatorics ,Primitive ring ,Simple ring ,0101 mathematics ,Quotient ring ,Mathematics - Abstract
The Nagata ring R(X) and the Serre’s conjecture ring R⟨X⟩ are two localizations of the polynomial ring R[X] at the polynomials of unit content and at the monic polynomials, respectively. In this pa...
- Published
- 2017
46. On prime rings whose central closure is finitely generated
- Author
-
Pjek-Hwee Lee, Edmund Puczyłowski, Wen-Fong Ke, and Mikhail A. Chebotar
- Subjects
Discrete mathematics ,Ring (mathematics) ,Algebra and Number Theory ,010102 general mathematics ,Zero (complex analysis) ,Closure (topology) ,010103 numerical & computational mathematics ,Center (group theory) ,01 natural sciences ,Prime (order theory) ,Associated prime ,Simple ring ,Prime ring ,0101 mathematics ,Mathematics - Abstract
The purpose of the paper is to study prime rings R such that the central closure RC is a simple ring with 1 and it is finitely generated over R by elements of the extended centroid C, that is, R C = R [ c 1 , … , c n ] , for some c 1 , … , c n ∈ C . In particular, we will show that if there exists a prime ring with zero center whose central closure is simple with 1 and generated by finitely many central elements, then there exists such a ring whose central closure is generated by two central elements.
- Published
- 2017
47. Derivation on Vinberg rings
- Author
-
Gangireddy Lakshmi Devi and Karamsi Jayalakshmi
- Subjects
Vinberg ring ,Pure mathematics ,Ring (mathematics) ,Endomorphism ,Mathematics::Commutative Algebra ,lcsh:Mathematics ,General Mathematics ,Mathematics::Rings and Algebras ,derivation ,Epimorphism ,lcsh:QA1-939 ,Algebra ,Nonassociative ring ,Mathematics::Group Theory ,Primitive ring ,simple ,Simple (abstract algebra) ,solid algebra ,Mathematics::Category Theory ,Simple ring ,Division ring ,Mathematics::Symplectic Geometry ,Associative property ,Mathematics - Abstract
A nonassociative ring which contains a well-known associative ring or left symmetric ring also known as Vinberg ring is of great interest. A method to construct Vinberg nonassociative ring is given; Vinberg nonassociative ring is shown as simple; all the derivations of nonassociative simple Vinberg algebra defined are determined; and finally in solid algebra it is shown that if is a nonzero endomorphism of , then is an epimorphism.
- Published
- 2017
48. A Dichotomy for the Gelfand–Kirillov Dimensions of Simple Modules over Simple Differential Rings
- Author
-
Arnab Dey Sarkar and Ashish Gupta
- Subjects
General Mathematics ,Mathematics::Rings and Algebras ,010102 general mathematics ,Dimension (graph theory) ,010103 numerical & computational mathematics ,01 natural sciences ,Algebra ,Simple (abstract algebra) ,Simple ring ,Lie algebra ,Gelfand–Kirillov dimension ,Differential algebra ,0101 mathematics ,Mathematics::Representation Theory ,Dimension theory (algebra) ,Simple module ,Mathematics - Abstract
The Gelfand–Kirillov dimension has gained importance since its introduction as a tool in the study of non-commutative infinite dimensional algebras and their modules. In this paper we show a dichotomy for the Gelfand–Kirillov dimension of simple modules over certain simple rings of differential operators. We thus answer a question of J. C. McConnell in Representations of solvable Lie algebras V. On the Gelfand-Kirillov dimension of simple modules. McConnell (J. Algebra 76(2), 489–493, 1982) concerning this dimension for a class of algebras that arise as simple homomorphic images of solvable lie algebras. We also determine the Gelfand–Kirillov dimension of an induced module.
- Published
- 2017
49. The ring of Colombeau’s full generalized quaternions
- Author
-
Antonio R. G. Garcia, Wagner Cortes, and S. H. da Silva
- Subjects
Mathematics::Functional Analysis ,Ring (mathematics) ,Ring theory ,Algebra and Number Theory ,Mathematics::Commutative Algebra ,Hurwitz quaternion ,010102 general mathematics ,Mathematics::Analysis of PDEs ,Semiprime ring ,01 natural sciences ,Algebra ,Colombeau algebra ,Simple ring ,0103 physical sciences ,Computer Science::Symbolic Computation ,010307 mathematical physics ,0101 mathematics ,Algebraic number ,Quaternion ,Computer Science::Distributed, Parallel, and Cluster Computing ,Mathematics - Abstract
In this paper, we introduce the ring of Colombeau full generalized quaternion, and we study its algebraic and topological properties. We prove that the ring of Colombeau full generalized quaternion...
- Published
- 2017
50. On the lattice of matric-extensible radicals. II.
- Author
-
Booth, G. L. and France-Jackson, H.
- Subjects
- *
LATTICE theory , *ASSOCIATIVE rings , *ATOMS , *RADICAL theory , *MATRICES (Mathematics) , *RING theory - Abstract
We continue our study of the lattice of matric-extensible radicals of associative rings. We find some atoms generated by simple rings of the lattices of all matric-extensible radicals, matric-extensible supernilpotent radicals and matric-extensible special radicals. We consider *-rings, which were previously defined by the second author, and consider when they generate atoms of these lattices. [ABSTRACT FROM AUTHOR]
- Published
- 2006
- Full Text
- View/download PDF
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