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We prove that a parabolic subgroup P contained in another parabolic subgroup P' of an Artin group A is a parabolic subgroup of P'. This answers a question of Godelle which is not obvious despite appearances. In order to achieve our result we construct a set-retraction A \to P of the inclusion map from a parabolic subgroup P into A. This retraction was implicitly constructed in a previous paper by Charney and the second author [Bull. Lond. Math. Soc. 46 (2014), pp. 1248–1255]. [ABSTRACT FROM AUTHOR]

Let X / s be a proper log smooth scheme of Cartier type over a fine log scheme whose underlying scheme is the spectrum of a perfect field κ of characteristic p > 0 . In this article we prove that the cohomology of 풲 ⁢ (풪 X) is a finitely generated 풲 ⁢ (κ) -module if the Yobuko height of X is finite. As an application of this result, we prove that, if the Yobuko height of a proper smooth threefold Y over κ is finite, then the crystalline cohomology of Y / κ has the Hodge–Witt decomposition and the p-primary torsion part of the Chow group of codimension 2 of Y is of finite cotype. These are nontrivial generalizations of results in [K. Joshi and C. S. Rajan, Frobenius splitting and ordinarity, Int. Math. Res. Not. IMRN 2003 2003, 2, 109–121] and [K. Joshi, Exotic torsion, Frobenius splitting and the slope spectral sequence, Canad. Math. Bull. 50 2007, 4, 567–578]. We also prove a fundamental inequality between the Artin–Mazur heights and the Yobuko height of X / s if X / s satisfies natural conditions. [ABSTRACT FROM AUTHOR]

In this paper we study the behavior of the Igusa–Todorov functions for Artin algebras A with finite injective dimension, and Gorenstein algebras as a particular case. We show that the ϕ -dimension and ψ -dimension are finite in both cases. Also we prove that monomial, gentle and cluster tilted algebras have finite ϕ -dimension and finite ψ -dimension. [ABSTRACT FROM AUTHOR]

In this paper, we prove an Artin type theorem for semigroups. Namely, we consider the concepts of hyperalternative and hyperassociative semigroups and prove that every two elements in any hyperalternative semigroup generate a hyperassociative subsemigroup. As a consequence, we characterize all hyperalternative semigroups, and prove that these semigroups form a variety of semigroups with four identities. [ABSTRACT FROM AUTHOR]

We show that the generalized W-modules defined in 2013 determine ∞A∞-components in the Auslander-Reiten quiver Γ(n, r) of the generalized Beilinson algebra B(n, r), n ≥ 3. These components entirely consist of modules with the constant Jordan type property. We arrive at this result by interpreting B(n, r) as an iterated one-point extension of the r-Kronecker algebra Kr, which enables us to generalize findings concerning the Auslander-Reiten quiver Γ(Kr) presented in 2013 to Γ(n, r). [ABSTRACT FROM AUTHOR]

We discuss the notion of strongly unbounded type for abelian length categories; this is closely related to the Second Brauer–Thrall Conjecture for Artin algebras. A new ingredient is the space of characters in the sense of Crawley-Boevey. [ABSTRACT FROM AUTHOR]

We prove that the Artin group A(235) is not coherent. [ABSTRACT FROM AUTHOR]

A necessary and sufficient condition for the existence of recollements of bounded Gorenstein derived categories of CM-finite orenstein Artin algebras is given. [ABSTRACT FROM AUTHOR]

We study the horofunction boundary of an Artin group of dihedral type with its word metric coming from either the usual Artin generators or the dual generators. In both cases, we determine the horoboundary and say which points are Busemann points, that is, the limits of geodesic rays. In the case of the dual generators, it turns out that all boundary points are Busemann points, but this is not true for the Artin generators. We also characterize the geodesics with respect to the dual generators, which allows us to calculate the associated geodesic growth series. [ABSTRACT FROM AUTHOR]

Let C be a faithfully balanced selforthogonal module over an Artin algebra R. We introduce the notion of n-C-star modules, which is a common generalization of n-star modules and n-C-tilting modules. We extend some characterizations of n-star modules to this context and prove that n-C-tilting modules are precisely n-C-star modules n-C-presenting all the injectives. [ABSTRACT FROM AUTHOR]

In this work, we will prove that the modules lying in a sectional bypass of an arrow in the Auslander-Reiten quiver of an artin algebra, are either all left stable or all right stable, but not τ-periodic. Moreover, if such a bypass exists, then the Auslander-Reiten quiver has an infinite left or right stable component which contains a section with a bypass. [ABSTRACT FROM AUTHOR]

In a recent paper, L.A. Bokut, V.V. Chaynikov and K.P. Shum have established a theorem of braid group Bn by applying Artin relations. For such a representation, it points out that all other compositions can be checked in the same way. In this note, we reconfirm such claim and check some more compositions. [ABSTRACT FROM AUTHOR]

We study a Z G-module A in the case where the group G is locally solvable and satisfies the condition min–naz and its cocentralizer in A is not an Artinian Z-module. We prove that the group G is solvable under the conditions indicated above. The structure of the group G is studied in detail in the case where this group is not a Chernikov group. [ABSTRACT FROM AUTHOR]

Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. However, the proof is non-constructive. The result is presented in two versions. The first version depends on Artin's Conjecture (1927) in Number Theory. The second version does not depend on conjectures not proved but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these results imply a similar result for quantum finite automata. [ABSTRACT FROM AUTHOR]

Abstract: Let R be a finite dimensional k-algebra over an algebraically closed field k and modR be the category of all finitely generated left R-modules. For a given full subcategory of modR, we denote by the projective finitistic dimension of . That is, . It was conjectured by H. Bass in the 60''s that the projective finitistic dimension has to be finite. Since then, much work has been done toward the proof of this conjecture. Recently, K. Igusa and G. Todorov defined in [K. Igusa, G. Todorov, On the finitistic global dimension conjecture for artin algebras, in: Representations of Algebras and Related Topics, in: Fields Inst. Commun., vol. 45, Amer. Math. Soc., Providence, RI, 2005, pp. 201–204] a function , which turned out to be useful to prove that is finite for some classes of algebras. In order to have a different approach to the finitistic dimension conjecture, we propose to consider a class of full subcategories of modR instead of a class of algebras. That is, we suggest to take the class of categories , of θ-filtered R-modules, for all stratifying systems in modR. We prove that the Finitistic Dimension Conjecture holds for the categories of filtered modules for stratifying systems with one or two (and some cases of three) modules of infinite projective dimension. [Copyright &y& Elsevier]

Abstract: Let be a ring and be an (infinite dimensional) partial tilting module. We show that the perpendicular category of is equivalent to the full module category where and is the Bongartz complement of modulo its -trace. Moreover, there is a ring epimorphism . We characterize the case when is a perfect localization. By [Riccardo Colpi, Alberto Tonolo, Jan Trlifaj, Partial cotilting modules and the lattices induced by them, Comm. Algebra 25 (10) (1997) 3225–3237], there exist mutually inverse isomorphisms and between the interval in the lattice of torsion classes in , and the lattice of all torsion classes in . We provide necessary and sufficient conditions for and to preserve tilting torsion classes. As a consequence, we show that these conditions are always satisfied when is a Dedekind domain, and if is finitely presented and is an artin algebra, then the conditions reduce to the trivial ones, namely that each value of and contains all injectives. [Copyright &y& Elsevier]

We classify thick subcategories of the bounded derived category of a hereditary abelian category A in terms of subcategories of A. The proof can be applied to characterize the localizing subcategories of the full derived category of A. As an application we prove an algebraic analog of the telescope conjecture for the derived category of a representation finite hereditary artin algebra. [ABSTRACT FROM AUTHOR]

In this paper we construct a gathering process by the means of which we obtain new normal forms in braid groups. The new normal forms generalize Artin–Markoff normal forms and possess an extremely natural geometric description. In the two last sections of the paper we discuss the implementation of the introduced gathering process and the questions that arose in our work. This discussion leads us to some interesting observations, in particular, we offer a method of generating a random braid. [ABSTRACT FROM AUTHOR]

For a given conformal algebra C , we write the correspondence between identities of the coefficient algebra Coeff C and identities of C itself as a pseudoalgebra. In particular, we write the defining relations of Jordan, alternative, and Mal'cev conformal algebras, and show that the analogue of the Artin's Theorem does not hold for alternative conformal algebras. [ABSTRACT FROM AUTHOR]

The notion of pure subgroup of an Artin group of finite type is introduced. The decidability of the generalized conjugacy problem for pure subgroups of Artin groups of finite type is proved. [ABSTRACT FROM AUTHOR]

A left orderable completely metrizable topological group is exhibited containing Artin's braid group on infinitely many strands. The group is the mapping class group (rel boundary) of the closed unit disk with a sequence of interior punctures converging to the boundary. This resolves an issue suggested by work of Dehornoy. [ABSTRACT FROM AUTHOR]

We study the asymptotic behaviour of the genus in some Artin-Schreier towers of function fields over a finite field, and we present a new class of Artin-Schreier towers having finite genus. [ABSTRACT FROM AUTHOR]

We consider the Magnus representation of the image of the pure braid group under the generalizations of the standard Artin representation, discovered by M. Wada. We will give a necessary and sufficient condition for the specialization of the reduced Wada's representation Gn(z) : Pn → GLn-1(ℂ) to be irreducible. It will be shown that for z = (z1,...,zn) ∈ (ℂ*)n, Gn(z) is irreducible if and only if z1k⋯znk ≠ 1. This is a generalization of our previous result concerning the irreducibility of the complex specialization of the reduced Gassner representation of Pn. [ABSTRACT FROM AUTHOR]

In this article, we give a simple combinatorial criterion allowing to verify whether a string algebra is shod or not. As a consequence, we classify all algebras with a discrete derived category which are derived equivalent to shod algebras. [ABSTRACT FROM AUTHOR]

We investigate a ring R with the property that for every right R-module M and every ideal I of R the annihilator of I in M is a direct summand of M, and determine conditions under which such a ring is semisimple Artinian. [ABSTRACT FROM AUTHOR]

Abstract: Let W be a finite irreducible Coxeter group and let be the classifying space for , the associated Artin group. If A is a commutative unitary ring, we consider the two local systems and over , respectively over the modules and , given by sending each standard generator of into the automorphism given by the multiplication by q. We show that and we generalize this relation to a particular class of algebraic complexes. We remark that is equal to the cohomology with trivial coefficients A of the Milnor fiber of the discriminant bundle of the associated reflection group. [Copyright &y& Elsevier]

In this paper, we study, for an artin algebra, the class (and ) which is a full subcategory of the category modA of finitely generated A-modules, and which consists of all indecomposable A-modules whose predecessors (and successors) have projective dimension (and injective dimension, respectively) at most one. We consider quotient algebras of A, which contain the information on these classes, then define and characterize those algebras for which the class is is contravariantly finite (and is covariantly finite, respectively). [Copyright &y& Elsevier]

In this paper, we investigate the minimal free resolution of certain level algebras which have minimal Hilbert Function among Artinian graded algebras of given socle degree and type. As a consequence of this results, we discover a new class of Hilbert Functions which do not support a unique smallest set of graded Betti numbers and another class which do not support all the possible resolutions between its maximum and minimum elements. [ABSTRACT FROM AUTHOR]

In this paper we consider a generalization of Vámos's proposition which asserts that finitely generated artinian and distributive modules are cyclic. Also, we show its duality as an answer to the problem which is shown by him (See Vámos, [Vámos, P. (1978). Finitely generated artinian and distributive modules are cyclic. Bull. London Math. Soc. 10(3):287–288]). [ABSTRACT FROM AUTHOR]

Let Γ be a connected component of the Auslander–Reiten quiver Γ(modA) of an Artin algebra. We show that Γ is quasi-directed if and only if the paths in indA, having end-points in Γ, satisfy certain conditions. Moreover, we describe the shapes of such components and identify the classes of algebras to which they are related. [Copyright &y& Elsevier]

We study whether the projective and injective properties of left R-modules can be implied to the special kind of left R[x]-modules, especially to the case of inverse polynomial modules and Laurent polynomial modules. [ABSTRACT FROM AUTHOR]

Twisting process for homogeneous algebras is defined. It consists of a particular kind of actual deformations controlled by a multiplicative cosimplicial quasicomplex C• related to each homogeneous algebra. The elements implementing twist transformations are a subclass of the counital 2-cocycles of C•. Such transformations are studied by means of their co-homological properties. It is shown they define an equivalence relation between homogeneous algebras, in such a way that cubic Artin–Schelter regular algebras of type S1 (including parafermionic and plactic algebras with two generators) belong to the same class. [Copyright &y& Elsevier]

New characterizations are found for Artinian, as well as for semiprimary rings. [ABSTRACT FROM AUTHOR]

We will show that any module over an artin algebra is a direct summand of some module whose endomorphism ring is quasi-hereditary. As a conclusion, any artin algebra has a finite representation dimension. [ABSTRACT FROM AUTHOR]

We show that the residual nilpotence of pure Artin groups of spherical type is easily deduced from the faithfulness of the Krammer–Digne representations. [ABSTRACT FROM AUTHOR]