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Abstract Let I ⊆ k [ x 1 , ... , x n ] be a squarefree monomial ideal in a polynomial ring. In this paper we study multiplications on the minimal free resolution F of k [ x 1 , ... , x n ] / I. In particular, we characterize the possible vectors of total Betti numbers for such ideals which admit a differential graded algebra (DGA) structure on F. We also show that under these assumptions the maximal shifts of the graded Betti numbers are subadditive. On the other hand, we present an example of a strongly generic monomial ideal which does not admit a DGA structure on its minimal free resolution. In particular, this demonstrates that the Hull resolution and the Lyubeznik resolution do not admit DGA structures in general. Finally, we show that it is enough to modify the last map of F to ensure that it admits the structure of a DG algebra. [ABSTRACT FROM AUTHOR]

A subgroup H of G is called complemented in G if there exists a subgroup K of G such that G = H K and H ∩ K = 1 . The aim of this paper is to prove the following: A finite group G is solvable if and only if its Sylow 3-, 5- and 7-subgroups are complemented in G . [ABSTRACT FROM AUTHOR]

A ring R is said to be left uniquely generated if R a = R b in R implies that a = u b for some unit u in R . These rings have been of interest since Kaplansky introduced them in 1949 in his classic study of elementary divisors. Writing l ( b ) = { r ∈ R | r b = 0 } , a theorem of Canfell asserts that R is left uniquely generated if and only if, whenever R a + l ( b ) = R where a , b ∈ R , then a − u ∈ l ( b ) for some unit u in R . By analogy with the stable range 1 condition we call a ring with this property left annihilator-stable. In this paper we exploit this perspective on the left UG rings to construct new examples and derive new results. For example, writing J for the Jacobson radical, we show that a semiregular ring R is left annihilator-stable if and only if R / J is unit-regular, an analogue of Bass' theorem that semilocal rings have stable range 1. [ABSTRACT FROM AUTHOR]

The object of study in this paper is the finite groups whose integral group rings have only trivial central units. Prime-power groups and metacyclic groups with this property are characterized. Metacyclic groups are also classified according to the central height of the unit groups of their integral group rings. [ABSTRACT FROM AUTHOR]

In this paper we give a general theorem that describes necessary and sufficient conditions for a module to satisfy the so-called Kadison–Dubois property. This is used to generalize Jacobi''s version of the Kadison–Dubois representation to associative rings. We apply this representation to obtain a noncommutative algebraic and geometric version of Putinar''s Positivstellensatz. We finish the paper by answering questions given by Marshall and Jacobi. [Copyright &y& Elsevier]

Abstract: In this paper, the cellularity of twisted semigroup algebras over an integral domain is investigated by introducing the concept of cellular twisted semigroup algebras of type . Partition algebras, Brauer algebras and Temperley–Lieb algebras all are examples of cellular twisted semigroup algebras of type . Our main result shows that the twisted semigroup algebra of a regular semigroup is cellular of type with respect to an involution on the twisted semigroup algebra if and only if the twisted group algebras of certain maximal subgroups are cellular algebras. Here we do not assume that the involution of the twisted semigroup algebra induces an involution of the semigroup itself. Moreover, for a twisted semigroup algebra, we do not require that the twisting decomposes essentially into a constant part and an invertible part, or takes values in the group of units in the ground ring. Note that trivially twisted semigroup algebras are the usual semigroup algebras. So, our results extend not only a recent result of East, but also some results of Wilcox. [Copyright &y& Elsevier]

Abstract: A double Ore extension is a natural generalization of the Ore extension. We prove that a connected graded double Ore extension of an Artin–Schelter regular algebra is Artin–Schelter regular. Some other basic properties such as the determinant of the DE-data are studied. Using the double Ore extension, we construct 26 families of Artin–Schelter regular algebras of global dimension four in a sequel paper. [Copyright &y& Elsevier]

Abstract: The maximal subalgebras of the finite-dimensional simple special Jordan superalgebras over an algebraically closed field of characteristic 0 are studied. This is a continuation of a previous paper by the same authors about maximal subalgebras of simple associative superalgebras, which is instrumental here. [Copyright &y& Elsevier]

Abstract: Let be linearly independent homogeneous polynomials in the standard -graded ring with the same degree and no common divisors. This defines a morphism . The Rees algebra of the ideal is the graded -algebra which can be described as the image of an -algebra homomorphism : . This paper discusses one result concerning the structure of the kernel of the map and its relation to the problem of finding the implicit equation of the image of the map given by , , . In particular, we prove a conjecture of Hong, Simis and Vasconcelos. We also relate our results to the theory of adjoint curves and prove a special case of a conjecture of Cox. [Copyright &y& Elsevier]

Abstract: In this paper we define model solvmanifold pairs and their diagonal type selfmaps in the tradition of Heath and Keppelmann. We derive an explicit formula for computing the relative Nielsen number on these spaces and selfmaps . We find that model solvmanifold pairs often exhibit interesting Schirmer theory, meaning . [Copyright &y& Elsevier]

Abstract: In this paper we characterize the minimal left ideals of a Leavitt path algebra as those which are isomorphic to principal left ideals generated by line points; that is, by vertices whose trees contain neither bifurcations nor closed paths. Moreover, we show that the socle of a Leavitt path algebra is the two-sided ideal generated by these line point vertices. This characterization allows us to compute the socle of certain algebras that arise as the Leavitt path algebra of a row-finite graph. A complete description of the socle of a Leavitt path algebra is given: it is a locally matricial algebra. [Copyright &y& Elsevier]

Abstract: Let be a hereditary abelian -category with tilting object and denote the bounded derived category of . This paper is devoted to a study of suspended subcategories of by means of their Ext-projectives. [Copyright &y& Elsevier]

Abstract: In this paper we study the adjoint functors between the category of Rota–Baxter algebras and the categories of dendriform dialgebras and trialgebras. In analogy to the well-known theory of the adjoint functor between the category of associative algebras and Lie algebras, we first give an explicit construction of free Rota–Baxter algebras and then apply it to obtain universal enveloping Rota–Baxter algebras of dendriform dialgebras and trialgebras. We further show that free dendriform dialgebras and trialgebras, as represented by binary planar trees and planar trees, are canonical subalgebras of free Rota–Baxter algebras. [Copyright &y& Elsevier]

Abstract: The notions of a perfect element and an admissible element of the free modular lattice generated by elements are introduced by Gelfand and Ponomarev in [I.M. Gelfand, V.A. Ponomarev, Free modular lattices and their representations, Collection of articles dedicated to the memory of Ivan Georgievic Petrovskii (1901–1973), IV. Uspehi Mat. Nauk 29 (6(180)) (1974) 3–58 (Russian); English translation: Russian Math. Surv. 29 (6) (1974) 1–56]. We recall that an element of a modular lattice is perfect, if for each finite-dimension indecomposable -linear representation over any field , the image of is either zero, or , where is the lattice of all vector -subspaces of . A complete classification of such elements in the lattice , associated to the extended Dynkin diagram (and also in , where ) is given in [I.M. Gelfand, V.A. Ponomarev, Free modular lattices and their representations, Collection of articles dedicated to the memory of Ivan Georgievic Petrovskii (1901–1973), IV. Uspehi Mat. Nauk 29 (6(180)) (1974) 3–58 (Russian); English translation: Russian Math. Surv. 29 (6) (1974) 1–56; I.M. Gelfand, V.A. Ponomarev, Lattices, representations, and their related algebras, I, Uspehi Mat. Nauk 31 (5(191)) (1976) 71–88 (Russian); English translation: Russian Math. Surv. 31 (5) (1976) 67–85; I.M. Gelfand, V.A. Ponomarev, Lattices, representations, and their related algebras, II. Uspehi Mat. Nauk 32 (1(193)) (1977) 85–106 (Russian); English translation: Russian Math. Surv. 32 (1) (1977) 91–114]. The main aim of the present paper is to classify all the admissible elements and all the perfect elements in the Dedekind lattice generated by six elements that are associated to the extended Dynkin diagram . We recall that in [I.M. Gelfand, V.A. Ponomarev, Free modular lattices and their representations, Collection of articles dedicated to the memory of Ivan Georgievic Petrovskii (1901–1973), IV. Uspehi Mat. Nauk 29 (6(180)) (1974) 3–58 (Russian); English translation: Russian Math. Surv. 29 (6) (1974) 1–56], Gelfand and Ponomarev construct admissible elements of the lattice recurrently. We suggest a direct method for creating admissible elements. Using this method we also construct admissible elements for and show that these elements coincide modulo linear equivalence with admissible elements constructed by Gelfand and Ponomarev. Admissible sequences and admissible elements for (resp. ) form 14 classes (resp. 8 classes) and possess some periodicity. Our classification of perfect elements for is based on the description of admissible elements. The constructed set of perfect elements is the union of -element distributive lattices , and is the distributive lattice itself. The lattice of perfect elements obtained by Gelfand and Ponomarev for can be imbedded into the lattice of perfect elements , associated with . Herrmann in [C. Herrmann, Rahmen und erzeugende Quadrupel in modularen Verbänden. (German) [Frames and generating quadruples in modular lattices], Algebra Universalis 14 (3) (1982) 357–387] constructed perfect elements , , in by means of some endomorphisms and showed that these perfect elements coincide with the Gelfand–Ponomarev perfect elements modulo linear equivalence. We show that the admissible elements in are also obtained by means of Herrmann’s endomorphisms . Herrmann’s endomorphism and the elementary map of Gelfand–Ponomarev act, in a sense, in opposite directions, namely the endomorphism adds the index to the beginning of the admissible sequence, and the elementary map adds the index to the end of the admissible sequence. [Copyright &y& Elsevier]

Abstract: In this paper we first give a lower bound on multiplicities for Buchsbaum homogeneous -algebras in terms of the dimension , the codimension , the initial degree , and the length of the local cohomology modules of . Next, we introduce the notion of Buchsbaum -algebras with minimal multiplicity of degree , and give several characterizations for those rings. In particular, we will show that those algebras have linear free resolutions. Further, we will give many examples of those algebras. [Copyright &y& Elsevier]

Abstract: The context for this paper is a class of distributive lattice expansions, called double quasioperator algebras (DQAs). The distinctive feature of these algebras is that their operations preserve or reverse both join and meet in each coordinate. Algebras of this type provide algebraic semantics for certain non-classical propositional logics. In particular, MV-algebras, which model the Łukasiewicz infinite-valued logic, are DQAs. Varieties of DQAs are here studied through their canonical extensions. A variety of this type having additional operations of arity at least 2 may fail to be canonical; it is already known, for example, that the variety of MV-algebras is not. Non-canonicity occurs when basic operations have two distinct canonical extensions and both are necessary to capture the structure of the original algebra. This obstruction to canonicity is different in nature from that customarily found in other settings. A generalized notion of canonicity is introduced which is shown to circumvent the problem. In addition, generalized canonicity allows one to capture on the canonical extensions of DQAs the algebraic operations in such a way that the laws that these obey may be translated into first-order conditions on suitable frames. This correspondence may be seen as the algebraic component of duality, in a way which is made precise. In many cases of interest, binary residuated operations are present. An operation which, coordinatewise, preserves and 0 lifts to an operation which is residuated, even when is not. If also preserves binary meet then the upper adjoints behave in a functional way on the frames. [Copyright &y& Elsevier]

Abstract: In this paper, we will show how to kill the obstructions to Lie algebra deformations via a method which essentially embeds a Lie algebra into a strong homotopy Lie algebra or algebra such that the sh-Lie algebra is the same homotopy type as the original Lie algebra. [Copyright &y& Elsevier]

Abstract: It is known from [M. Auslander, M.I. Platzeck, I. Reiten, Coxeter functors without diagrams, Trans. Amer. Math. Soc. 250 (1979) 1–46] and [C.M. Ringel, PBW-basis of quantum groups, J. Reine Angew. Math. 470 (1996) 51–85] that the Bernstein–Gelfand–Ponomarev reflection functors are special cases of tilting functors and these reflection functors induce isomorphisms between certain subalgebras of Ringel–Hall algebras. In [A. Wufu, Tilting functors and Ringel–Hall algebras, Comm. Algebra 33 (1) (2005) 343–348] the result from [C.M. Ringel, PBW-basis of quantum groups, J. Reine Angew. Math. 470 (1996) 51–85] is generalized to the tilting module case by giving an isomorphism between two Ringel–Hall subalgebras. In [J. Miyashita, Tilting Modules of Finite Projective Dimension, Math. Z. 193 (1986) 113–146] Miyashita generalized the tilting theory by introducing the tilting modules of finite projective dimension. In this paper the result in [A. Wufu, Tilting functors and Ringel–Hall algebras, Comm. Algebra 33 (1) (2005) 343–348] is generalized to the tilting modules of finite projective dimension. [Copyright &y& Elsevier]

Abstract: In this paper we introduce a new technique to study associated graded modules. Let be a Noetherian local ring with . Our techniques give a necessary and sufficient condition for for all . Other applications are also included; most notable is an upper bound regarding the Ratliff–Rush filtration. [Copyright &y& Elsevier]

Abstract: Let be a compactification of an affine 3-fold into a smooth projective 3-fold such that the (reduced) boundary divisor is SNC. In this paper, as an affine counterpart to the work due to S. Mori (cf. [S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982) 133–176]), we shall classify -negative extremal rays on . In particular, if such an extremal ray intersects non-negatively, we shall describe the log flips and divisorial contractions appearing explicitly. [Copyright &y& Elsevier]

Abstract: Abstract Cogalois Theory for arbitrary profinite groups was initiated by T. Albu and Ş.A. Basarab [An Abstract Cogalois Theory for profinite groups, J. Pure. Appl. Algebra 200 (2005) 227–250]. The aim of this paper is twofold: firstly, to present the abstract group theoretic versions of various types of Kummer field extensions, and secondly, to show how some basic results of the (Field Theoretic) Cogalois Theory can be very easily deduced from their abstract versions. [Copyright &y& Elsevier]

Abstract: In this paper we study the multigraded Hilbert and Poincaré–Betti series of , where is the ring of polynomials in indeterminates divided by the monomial ideal . There is a conjecture about the multigraded Poincaré–Betti series by Charalambous and Reeves which they proved in the case where the Taylor resolution is minimal. We introduce a conjecture about the minimal -free resolution of the residue class field and show that this conjecture implies the conjecture of Charalambous and Reeves and, in addition, gives a formula for the Hilbert series. Using Algebraic Discrete Morse theory, we prove that the homology of the Koszul complex of with respect to is isomorphic to a graded commutative ring of polynomials over certain sets in the Taylor resolution divided by an ideal of relations. This leads to a proof of our conjecture for some classes of algebras . We also give an approach for the proof of our conjecture via Algebraic Discrete Morse theory in the general case. The conjecture implies that is Golod if and only if the product (i.e. the first Massey operation) on the Koszul homology is trivial. Under the assumption of the conjecture we finally prove that a very simple purely combinatorial condition on the minimal monomial generating system of implies Golodness for . [Copyright &y& Elsevier]

Abstract: Let be a reduced curve singularity. is called of finite self-dual type if there exist only finitely many isomorphism classes of indecomposable, self-dual, torsion-free modules over the local ring of . In this paper it is shown that the singularities of finite self-dual type are those which dominate a simple plane singularity. [Copyright &y& Elsevier]

Abstract: For a finite set of points and for a given point , the notion of a separator of in (a hypersurface containing all the points in except ) and of the degree of in , (the minimum degree of these separators) has been largely studied. In this paper we extend these notions to a set of points on a projectively normal surface , considering as separators arithmetically Cohen–Macaulay curves and generalizing the case in a natural way. We denote the minimum degree of such curves as and we study its relation to . We prove that if is a variety of minimal degree these two terms are explicitly related by a formula, whereas only an inequality holds for other kinds of surfaces. [Copyright &y& Elsevier]

Abstract: Let I be an equimultiple ideal of Noetherian local ring A. This paper gives some multiplicity formulas of the extended Rees algebras In the case A generalized Cohen–Macaulay, we determine when T is Cohen–Macaulay and as an immediate consequence we obtain e.g., some criteria for the Cohen–Macaulayness of Rees algebra over a Cohen–Macaulay ring in terms of reduction numbers and ideals. [Copyright &y& Elsevier]

Abstract: The first purpose of this paper is to set up a general notion of skew power series rings S over a coefficient ring R, which are then studied by filtered ring techniques. The second goal is the investigation of the class of S-modules which are finitely generated as R-modules. In the case that S and R are Auslander regular we show in particular that the codimension of M as S-module is one higher than the codimension of M as R-module. Furthermore its class in the Grothendieck group of S-modules of codimension at most one less vanishes, which is in the spirit of the Gersten conjecture for commutative regular local rings. Finally we apply these results to Iwasawa algebras of p-adic Lie groups. [Copyright &y& Elsevier]

Abstract: In this paper, we extend a previous result of A. Pillay and the author regarding existence of rational points over elliptic and hyperelliptic curves with generic moduli defined over supersimple fields to the even characteristic case. We give a detailed exposition of the affine models of these families of curves in characteristic 2 and the transformations between members in the same rational isomorphism class. [Copyright &y& Elsevier]

Abstract: In the present paper, we study the nonzero level Harish-Chandra modules for the Virasoro-like algebra. We prove that a nonzero level Harish-Chandra module of the Virasoro-like algebra is a generalized highest weight (GHW for short) module. Then we prove that a GHW module of the Virasoro-like algebra is induced from an irreducible module of a Heisenberg subalgebra. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the dimension theory of tensor products of algebras over a field k. In fact, we provide a formula for the Krull dimension of when A and B are k-algebras such that is an AF-domain for some positive integer n. As an application, we construct a new family of k-algebras A and B for which dim() may be computed. [Copyright &y& Elsevier]

Abstract: In the paper a generalization of the known construction of trivial extension algebras is introduced. For the new constructed algebras one can indicate a construction of their Galois coverings. As an application of these constructions one can obtain a nice Galois coverings for the enveloping algebras of trivial extension algebras of triangular algebras. [Copyright &y& Elsevier]

Abstract: Let , be positive integers such that and be a field. We consider all pairs where is a finite dimensional -bounded -module and is a submodule of which is -bounded. They form the objects of the submodule category which is a Krull–Schmidt category with Auslander–Reiten sequences. The case deals with submodules of -modules and has been studied well. In this paper we determine the representation type of the categories also for the cases where : It turns out that there are only finitely many indecomposables in if either , , or ; the category is tame if is one of the pairs , , , or ; otherwise, has wild representation type. Moreover, in each of the finite or tame cases we describe the indecomposables and picture the Auslander–Reiten quiver. [Copyright &y& Elsevier]

Abstract: This paper gives criteria for a Cohen–Macaulay local ring to be Gorenstein, in terms of the vanishing of Ext modules. The main results extend earlier work of Ulrich. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to classify irreducible integrable modules of the full toroidal Lie-algebras, with finite-dimensional weight spaces and non-zero central charge. [Copyright &y& Elsevier]

Abstract: Let A be an integral k-algebra of finite type over a field k of characteristic zero. Let be a family of k-derivations on A and the A-module spanned by . In this paper, we generalise a result due to Nowicki and construct an element of such that . Such a derivation is called -minimal. Then we establish a density theorem for -minimal derivations in . [Copyright &y& Elsevier]

Abstract: Let K be a field of characteristic zero, and let be a purely transcendental field extension of K of transcendence degree . Lüroth''s Theorem. Let E be a subfield of that properly contains the field K. Then for a transcendental element . A field extension is called a Lüroth field extension if and every subfield with is a rational function field in one variable. In this paper, we prove Theorem 1. If F is a Lüroth field extension of field K of characteristic zero that coincides with it''s algebraic closure in F then so is a purely transcendental field extension . As a consequence of this result we have a description of integrally closed subalgebras of of dimension 1. Theorem 2. Suppose, in addition, that K is an algebraically closed field. Let R be a K-subalgebra of the field that is integrally closed in and the transcendence degree of its field of fractions is 1 over K. Then there exists a transcendental element over K such that . [Copyright &y& Elsevier]

Abstract: Let be an algebraically closed field of an arbitrary characteristic. In this paper, we show that the Jelonek set of a polynomial generically finite map (i.e. the set of points at which the map f is not finite) is a -uniruled variety of pure dimension or the empty set. We also give an example that it is not necessarily separably uniruled although the map is separable. [Copyright &y& Elsevier]

Abstract: Algebra extensions where A is a left B-module such that the B-action extends the multiplication in A are ubiquitous. We encounter examples of such extensions in the study of group actions, group gradings or more general Hopf actions as well as in the study of the bimodule structure of an algebra. In this paper we are extending R.Wisbauer''s method of constructing the central closure of a semiprime algebra using its multiplication algebra to those kinds of algebra extensions. More precisely if A is a k-algebra and B some subalgebra of that contains the multiplication algebra of A, then the self-injective hull of A as B-module becomes a k-algebra provided A does not contain any nilpotent B-stable ideals. We show that under certain assumptions can be identified with a subalgebra of the Martindale quotient ring of A. This construction is then applied to Hopf module algebras. [Copyright &y& Elsevier]

Abstract: Let R be a ring and be a polynomial in noncommutative indeterminates with coefficients from and zero constant. The ring R is said to be an f-ring if for all of R and a virtually f-ring if for every n infinite subsets (not necessarily distinct) of R, there exist n elements such that . Let be the ‘smallest’ ring (in some sense) with identity containing R such that . Then denote by the subring generated by the identity of and denote by the image of f in (the ring of polynomials with coefficients in in commutative indeterminates ). In this paper, we show that if R is a left primitive virtually f-ring such that , then R is finite. Using this result, we prove that an infinite semisimple virtually f-ring R is an f-ring, if the subring of generated by the coefficients of is equal to ; and we also prove that if , where , then every infinite virtually f-ring with identity is a commutative f-ring. Finally we show that a commutative Noetherian virtually f-ring R with identity is finite if the subring generated by the coefficients of is . [Copyright &y& Elsevier]

Abstract: Hansen (Appl. Algebra Eng. Comm. Comput. 14 (2003) 175) uses cohomological methods to find a lower bound for the minimum distance of an evaluation code determined by a reduced complete intersection in . In this paper, we generalize Hansen''s results from to ; we also show that the hypotheses of Hansen (2003) may be weakened. The proof is succinct and follows by combining the Cayley–Bacharach Theorem and the bounds on evaluation codes obtained in Hansen (Zero-Dimensional Schemes (Ravello, 1992), de Gruyter, Berlin, 1994, pp. 205–211). [Copyright &y& Elsevier]

Abstract: This paper is concerned with two applications of bases of Riemann–Roch spaces. In the first application, we define the floor of a divisor and obtain improved bounds on the parameters of algebraic geometry codes. These bounds apply to a larger class of codes than that of Homma and Kim (J. Pure Appl. Algebra 162 (2001) 273). Then we determine explicit bases for large classes of Riemann–Roch spaces of the Hermitian function field. These bases give better estimates on the parameters of a large class of -point Hermitian codes. In the second application, these bases are used for fast implementation of Xing and Niederreiter''s method (Acta. Arith. 72 (1995) 281) for the construction of low-discrepancy sequences. [Copyright &y& Elsevier]

Let R be a field with characteristic zero. In this paper it is proved that power linear Keller maps Rn→Rn with rank at most two are linearly triangularizable. [Copyright &y& Elsevier]

Around 1980 two generalizations of the theory of linearly ordered fields appeared in the literature: Becker''s theory of orderings of higher level on fields (J. Reine Angew. Math. 307/308 (1979)8) and Holland''s theory of *-orderings on skew-fields with involution (J. Algebra 101 (1) (1986) 16–46). The aim of this paper is to unify both theories.In Section 1 we define (higher level) *-signatures on domains with involution which correspond to higher level preorderings in Becker''s theory. The subclasses of 2-cyclic and cyclic *-signatures correspond to complete preorderings and orderings respectively. We prove a necessary and sufficient condition for extendability of *-signatures from Ore domains to skew-fields of fractions.In Section 2 we define the set of bounded elements of a *-signature on a skew field with involution. If the skew field contains a central element i such that i2=-1 and i*=-i and the *-signature is 2-cyclic then the set of bounded elements is an invariant valuation ring. An example shows that the assumption on i cannot be omitted.In Section 3 we define extended *-signatures and prove that every 2-cyclic *-signature on a skew field D with i∈Z(D) is a restriction of some extended *-signature.In Section 4 we define extended *-preorderings as positive cones of extended *-signatures. We show that every *-preordering which is a restriction of an extended *-preordering is equal to the intersection of all *-orderings containing it. The assumption i∈Z(D) is not required.Section 5 presents auxilliary material for the proof of the weak isotropy principle for higher level *-signatures which is given in Section 6. [Copyright &y& Elsevier]

Let K be a field of characteristic zero, let A, B be K-algebras with polynomial identity and let M be a free (A,B)-bimodule. The algebra R=A/0 M/B can be endowed with a natural Z2-grading. In this paper, we compute the graded cocharacter sequence, the graded codimension sequence and the superexponent of R. As a consequence of these results, we also study the above PI-invariants in the setting of upper triangular matrices. In particular, we completely classify the algebra of 3×3 upper triangular matrices endowed with all possible Z2-gradings. [Copyright &y& Elsevier]

In this paper, we consider how the ∇-, Δ- and global dimensions of a quasi-hereditary algebra are interrelated. We first consider quasi-hereditary algebras with simple preserving duality and such that if μ<λ then ∇.f.d.(L(μ))<∇.f.d.(L(λ)), where μ, λ are in the poset and L(μ), L(λ) are the corresponding simples. We show that in this case the global dimension of the algebra is twice its ∇-filtration dimension. We then consider more general quasi-hereditary algebras and look at how these dimensions are affected by the Ringel dual and by two forms of truncation. We restrict again to quasi-hereditary algebras with simple preserving duality and consider various orders on the poset compatible with quasi-hereditary structure and the ∇-, Δ- and injective dimensions of the simple and the costandard modules. [Copyright &y& Elsevier]

In this paper we introduce the notion of Jordan system (algebra, pair or triple system) of Martindale-like quotients with respect to a filter of ideals as that whose elements are absorbed into the original system by ideals of the filter, and prove that it inherits regularity conditions such as (semi)primeness and nondegeneracy. When we consider power filters of sturdy ideals, the notions of Jordan systems of Martindale-like quotients and Lie algebras of quotients are related through the Tits–Kantor–Koecher construction, and that allows us to give constructions of the maximal systems of quotients when the original systems are nondegenerate. [Copyright &y& Elsevier]

In this paper we study dual coalgebras of algebras over arbitrary (Noetherian) commutative rings. We present and study a generalized notion of coreflexive comodules and use the results obtained for them to characterize the so called coreflexive coalgebras. Our approach in this note is an algebraically topological one. [Copyright &y& Elsevier]

We use the class of representation-finite algebras to investigate the finitistic dimension conjecture. In this way we obtain a large class of algebras for which the finitistic dimension conjecture holds. The main results in this paper are: (1) Let A be an artin algebra and let Ij,1⩽j⩽n be a family of ideals in A with I1I2⋯In=0, such that proj.dim(AIj)<∞ and proj.dim(Ij)A=0 for all j⩾3. If A/I1 and A/I2 are representation-finite and if A/Ij has finite finitistic dimension for j⩾3, then the finitistic dimension of A is finite. In particular, the finitistic dimension conjecture is true for algebras obtained from representation-finite algebras by forming dual extensions, trivially twisted extensions, Hochschild extensions, matrix algebras and tensor products with algebras of radical-square-zero. (2) Let A,B and C be three artin algebras with the same identity such that (i) C⊆B⊆A, and (ii) the Jacobson radical of C is a left ideal of B and the Jacobson radical of B is a left ideal of A. If A is representation-finite, then C has finite finitistic dimension. We also provide a way to construct algebras satisfying all conditions in (2), and this leads to a new reformulation of the finitistic dimension conjecture. [Copyright &y& Elsevier]

In this paper we study d-Koszul algebras which were introduced by Berger. We show that when d⩾3, these are classified by the Ext-algebra being generated in degrees 0, 1, and 2. We show the Ext-algebra, after regrading, is a Koszul algebra and present the structure of the Ext-algebra. [Copyright &y& Elsevier]

A rational affine parametrization of an algebraic surface establishes a rational correspondence of the affine plane with the surface. We consider the problem of computing the degree of such a rational map. In general, determining the degree of a rational map can be achieved by means of elimination theoretic methods. For curves, it is shown that the degree can be computed by gcd computations. In this paper, we show that the degree of a rational map induced by a surface parametrization can be computed by means of gcd and univariate resultant computations. The basic idea is to express the elements of a generic fibre as the finitely many intersection points of certain curves directly constructed from the parametrization, and defined over the algebraic closure of a field of rational functions. [Copyright &y& Elsevier]

In this paper, we determine a presentation by explicit generators and relations for the Dade group of all (almost) extraspecial p-groups. The proof of the main result uses the cohomological properties of the Tits building corresponding to the natural geometric structure of the lattice of subgroups of such p-groups. [Copyright &y& Elsevier]