Abstract We construct an isomorphism between the partially ordered set of tilting modules for the Auslander algebra of K[x]/(xn) and the interval of rational permutation braids in the braid group on n strands. Hence, there are only finitely many tilting modules.

Abstract In this paper, we study the class of free multiarrangements of hyperplanes. Specifically, we investigate the relations between freeness over a field of finite characteristic and freeness over Q.

Abstract Let (R,m) be a local ring and C be a semidualizing module such that C≅HomR(M,R) for some finitely generated R-module M. We study some properties of M and C. It is shown that if R is Cohen–Macaulay and ExtRi(M,R)=0 for 1≤i≤dim R, then M≅C≅R. Also, it is proved that if R is a one-dimensional Cohen–Macaulay ring, then C≅R.

Abstract Let F be a free group of rank d≥2. Consider the quotient F/[γ4(F′),F]F″′, the free centre-by-(nilpotent of class 3)-by-abelian group within the variety of all soluble groups of derived length 3. A peculiar feature of this group is the occurence of torsion in its centre. Our main result is a complete description of an elementary abelian 2-group of rank (d4) in F/[γ4(F′),F]F″′ in terms of generators

Abstract Let Λ be an artin algebra and let PΛ<∞ the category of finitely generated right Λ-modules of finite projective dimension. We show that PΛ<∞ is contravariantly finite in if and only if the direct sum E of the indecomposable Ext mod Λ-injective modules in PΛ<∞ form a tilting module in mod Λ. Moreover, we show that in this case E coincides with the direct sum of the minimal right PΛ<∞-approximations

Abstract In this corrigendum, statement (5) of Proposition 4.4 is reformulated and an example is given to show that this correction is necessary.

Abstract We introduce a concept of 3-Lie-Rinehart superalgebra and systematically describe a cohomology complex by considering coefficient modules. Furthermore, we study the relationships between a Lie-Rinehart superalgebra and its induced 3-Lie-Rinehart superalgebra. The deformations of 3-Lie-Rinehart superalgebra are considered via a cohomology theory.

Abstract We distinguish 2-maximal and strictly 2-maximal subgroups of a finite group and give examples of soluble and simple groups in which every 2-maximal subgroup is strictly 2-maximal. Let M be a maximal subgroup of a group G. We prove that every maximal subgroup of M is strictly 2-maximal in G if M is normal in G or if G is p-soluble and |G:M|=p. We describe the structure of a finite group in

Abstract Gabriel showed that for a unital ring R, there exists a bijective correspondence between the set of Gabriel filters of R and the set of Giraud subcategories of Mod(R). In this paper we prove a result analogous to the one given by Gabriel: for a small preadditive category C, there exists a bijective correspondence between the left Gabriel filters of C and Giraud subcategories of Mod(C).

Abstract Hyperhomology is applied to give explicit constructions of left or right adjoint functors of some inclusions between unbounded homotopy categories of additive categories arising from cotorsion pairs in abelian categories. These constructions are independent of Brown representability and do not involve cardinality in set theory. Applications are then given to injective cotorsion pairs in abelian

Abstract Abundant semigroups containing multiplicative ample transversals are introduced by the author. Guo establishes the structure of abundant semigroups with multiplicative adequate transversals. As any ample semigroup is adequate, is Guo’s structure an extension of that introduced by the author? After answering this question positively and providing a natural order for the multiplicative ample

Abstract The goal of this work is to introduce the notion of 3-Hom-L-dendriform algebras which is the dendriform version of 3-Hom-Lie-algebras. They can be also regarded as the ternary analogous of Hom-L-dendriform algebras. We give the representation of a 3-Hom-pre-Lie algebra. Moreover, we introduce the notion of Nijenhuis operators on a 3-Hom-pre-Lie algebra and provide some constructions of 3-Hom-L-dendriform

Abstract Given a group G and an endomorphism φ of G, two elements x,y∈G are said to be φ-conjugate if x=gyφ(g)−1 for some g∈G. The number of equivalence classes for this relation is the Reidemeister number R(φ) of φ. The set {R(ψ)|ψ∈Aut(G)} is called the Reidemeister spectrum of G. We investigate Reidemeister numbers and spectra on direct products of finitely many groups and determine what information

Abstract Let (K, v) be a Henselian valued field. In this article, we use Okutsu sequences for monic, irreducible polynomials in K[x], and their relationship with MacLane chains of inductive valuations on K[x], to obtain some results on the computation of invariants of algebraic elements over K.

Abstract In this paper, a semigroup algebra consisting of polynomial expressions with coefficients in a field F and exponents in an additive submonoid M of Q≥0 is called a Puiseux algebra and denoted by F[M]. Here we study the atomic structure of Puiseux algebras. To begin with, we answer the isomorphism problem for the class of Puiseux algebras, that is, we show that for a field F if two Puiseux algebras

Abstract In this note, we prove the inductive blockwise Alperin weight condition for PSU(4,3) by establishing an equivariant bijection between 2-irreducible Brauer characters and 2-weights of the 2′-cover of PSU(4,3) and for PSU(6,2) by establishing an equivariant bijection between 3-irreducible Brauer characters and 3-weights of the 3′-cover of PSU(6,2). Thus the inductive blockwise Alperin weight

Abstract I correct a slip in an argument in the above paper. This does not affect the main result: the Gerstenhaber Problem is Turing computable for all fields.

Abstract In this article, we prove that if R is a proper alternative ring whose additive group has no 3-torsion and whose non-zero commutators are not zero-divisors, then R has no zero-divisors. It follows from a theorem of Bruck and Kleinfeld that if, in addition, the characteristic of R is not 2, then the central quotient of R is an octonion division algebra over some field. We include other characterizations

Abstract The present paper is devoted to studying 2-local superderivations on the super Virasoro algebra and the super W(2,2) algebra. It is proved that all 2-local superderivations on the super Virasoro algebra as well as the super W(2,2) algebra are (global) superderivations.

Abstract In this article, we describe a criterion for an element of the dual space of an algebra to belong to the finite dual. This result is used to study when a certain subspace of the dual space is a subcoalgebra of the finite dual. We further apply it to find a right alternative coalgebra that is not locally finite. This work is motivated by a conjecture from I. Shestakov, which states that all

Abstract We investigate connections between von Neumann regularity of endomorphisms and perspectivity of direct summands in modules. This leads to a new classification of those rings whose regular elements are strongly regular, which turn out to be exactly the rings R whose idempotents are central modulo the Jacobson radical J(R). An important component of our work is an investigation of the left and

Abstract Let R be an affine Poisson algebra over a field of characteristic zero and let A be a Poisson order over R. It is proved that every Poisson primitive ideal of A is annihilator of a simple Poisson A-module.

Abstract Let φ and ψ be regular quadratic forms over a field F of characteristic different from 2. We say that ψ is a quasisubform of φ if there is a∈F* such that aψ is a subform of φ. Let L/F be an odd degree field extension. Assume that ψL is a quasisubform of φL. A natural question is whether ψ is a quasisubform of φ. We give a positive answer to this question in any of the following cases: The

Abstract This paper is devoted to the study of four-dimensional commutative power-associative non-Jordan train algebras. The existence of a unique orthogonal idempotent element in such kind of algebras enables us to define a non-zero algebra homomorphism over their ground field, which gives rise to train algebras of rank 4. We describe the irreducible representations over an algebraically closed field

Abstract Adachi et al. have introduced support τ-tilting pairs from the viewpoint of mutation. Let (A, T, B) be a tilting triple. In this article, it is proved that there is a bijection between the left mutations of a basic support τ-tilting module T and the indecomposable splitting projective objects of FacT, in the sense of Auslander and Smalø. If T is a separating and splitting tilting module, then

Abstract Factor systems are a tool for working on the extension problem of algebraic structures such as groups, Lie algebras, and associative algebras. Their applications are numerous and well-known in these common settings. We construct P algebra analogues to a series of results from W. R. Scott’s Group Theory, which gives an explicit theory of factor systems for the group case. Here P ranges over

Abstract Let R be a noncommutative prime ring equipped with an antiautomorphism f such that (i) [f(xk), xm] = 0, all x ∈ R, where k, m are fixed positive integers. In this article, we establish that from (i) follows (ii) [f(x), x = 0, all x ∈ R. More is to be said about the type of f and the structure of R.

Abstract In this article, we use quite elementary and simple ideas to rebuild and study the patch and flat topologies on the prime spectrum from a natural point of view (this new approach is based on the significant applications of the power set ring). Especially, the proof of a major result in the literature on the comparison of topologies greatly simplified and shortened. Also a new characterization

Abstract For the second fundamental representation of the general linear group over a commutative ring R, we construct straightforward and uniform polynomial expressions of elementary generators as products of elementary conjugates of an arbitrary matrix and its inverse. Toward the solution, we get stabilization theorems for any column of a matrix from GL(n2)(R) or from the exterior square of GLn(R)

Abstract Let X be a semibrick in an extriangulated category C. Let T be the filtration subcategory generated by X. We give a one-to-one correspondence between simple semibricks and length wide subcategories in C. This generalizes a bijection given by Ringel in module categories, which has been generalized by Enomoto to exact categories. Moreover, we also give a one-to-one correspondence between cotorsion

Abstract A ring R will be called dagger if a2−b2∈4R⇒a−b∈2R holds in R. We will show that any 2-integrally closed domain is dagger, and that, when the characteristic is not two, a 2-root closed and dagger domain is 2-integrally closed. Examples and non-examples of dagger domains are constructed.

Abstract A commutative ring R is stable if every non-zero ideal I of R is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have received wide attention in the literature ever since then. Much is known on the algebraic structure of stable rings and on the relationship of stability with other algebraic properties such as divisoriality and the 2-generator

Abstract In this article, we find a family SLn,m, in any arbitrary dimensions, of cohomologically rigid solvable Lie superalgebras with nilradical the model filiform Lie superalgebra Ln,m. Moreover, we exhibit a family of cohomologically rigid solvable Lie superalgebras with nilradical the model nilpotent Lie superalgebra of generic characteristic sequence. Both cases correspond to solvable Lie superalgebras

Abstract Our first aim is to provide an analog of the Gabriel-Quillen embedding theorem for n-exact categories. Also we give an example of an n-exact category that in not an n-cluster tilting subcategory, and we suggest two possible ways for realizing n-exact categories as n-cluster tilting subcategory.

Abstract A ring extension is a ring homomorphism preserving identities. In this paper, we give the definition of relatively free modules on ring extensions and develop some basic properties of relatively free modules. Then we establish the relationship between relatively free modules and relatively projective modules. In particular, we prove that the relatively free modules, relatively projective modules

Abstract Axial algebras are a class of commutative non-associative algebras generated by idempotents, called axes, with adjoint action semi-simple and satisfying a prescribed fusion law. Axial algebras were introduced by Hall, Rehren and Shpectorov (in 2015) as a broad generalization of Majorana algebras of Ivanov, whose axioms were derived from the properties of the Griess algebra for the Monster

Abstract In this exposition, we propose a notion of rank and rigidity of locally nilpotent derivations of affine fibrations. We show that the concept is analogous to the perception of rank and rigidity of locally nilpotent derivations of polynomial algebras. Our results characterize locally nilpotent derivations of A3-fibrations having slice by classifying the fixed point free locally nilpotent derivations

Abstract Let (R,m) be a complete commutative Noetherian local ring, I an ideal of R, M an R-module (not necessarily I-torsion) and N a finitely generated R-module with SuppR(N)⊆V(I). It is shown that if M is I-ETH-cominimax (i.e. ExtRi(R/I,M) is minimax (or Matlis reflexive), for all i≥0) and dim M≤1 or more generally M∈FD≤1, then the R-module ExtRn(M,N) is finitely generated, for all n≥0. As an application

Abstract We characterize colour-preserving automorphism vertex transitivity and vertex transitivity of the Cayley graphs of all semigroups in a class of pseudo-unitary homogeneous semigroups.

Abstract We present an explicit minimal set of generators for the defining ideal of the family of Backelin semigroups and find its Betti numbers. In particular, we compute the type of the semigroup as well, correcting a claim in the literature. Additionally, we show that the Betti numbers of the corresponding numerical semigroup ring coincide to those of its tangent cone.

Abstract An element a in a *-ring R has *-DMP inverse if there exists m∈N such that am∈R#∩R† and (am)#=(am)†. If m = 1, then a is said to have *-gMP inverse. In this paper, we present several new characterizations of *-DMP inverses in a *-ring. We prove that a has *-DMP inverse if and only if there exists a projection e∈comm(a) such that a+e∈R−1 and ae is nilpotent if and only if there exist m∈N and

Abstract A class of finite-dimensional Hopf algebras which generalize the notion of Taft algebras is studied. We give necessary and sufficient conditions for these Hopf algebras to omit a pair in involution. That is, to not have a group-like and a character implementing the square of the antipode. As a consequence, we prove the existence of an infinite set of examples of finite-dimensional Hopf algebras

Abstract We study the subvariety of singular sections, the discriminant, of a base point free linear system |L| on a smooth toric variety X. On one hand we describe pairs (X, L) for which the discriminant is of low dimension. Precisely, we collect some bounds on this dimension and classify those pairs whose dimension differs the bound less than or equal to two. On the other hand we study the degree

Abstract We introduce and study (dual) relative F-Baer objects as specializations of (dual) relative split objects with respect to a fully invariant short exact sequence in AB3* (AB3) abelian categories. We analyze their relationship with (dual) relative Baer objects, and we study direct summands and direct sums of (dual) relative F-Baer objects. We give applications to module and comodule categories

Abstract We classify all decompositions of M3(C) into a direct vector–space sum of two subalgebras such that one of the subalgebras contains the identity matrix.

Abstract Let R be a commutative Artinian ring and let ΓE(R) be the compressed zero-divisor graph associated to R. The question of when the clique number ω(ΓE(R))<∞ was raised by J. Coykendall, S. Sather-Wagstaff, L. Sheppardson, and S. Spiroff. They proved that if ℓ(R)≤4 (where ℓ(R) is the largest length of any of its chains of ideals), then ω(ΓE(R))<∞. When ℓ(R)=6, they gave an example of a local

Abstract We give a necessary and sufficient condition for the nonsingular projective toric variety associated to the graph cubeahedron of a finite simple graph to be Fano or weak Fano in terms of the graph.

Abstract Let G be a finite group and let Irr(G) be the set of all irreducible complex characters of G. For a character χ∈Irr(G), the number cod(χ):=|G:ker(χ)|/χ(1) is called the co-degree of χ. The set of co-degrees of all irreducible characters of G is denoted by cod(G). In this paper, we show that for a nontrivial finite group G, |Irr(G)|=|cod(G)| if and only if G is isomorphic to Z2 or S3.

Abstract Our first result provides a new characterization of Auslander algebras using a property of hereditary torsion pairs. The second result shows an Auslander algebra Λ is left or right glued if and only if Λ is representation-finite. Finally, our third result shows the module category of any Auslander algebra contains a tilting module with a particular property, which we call the hereditary property

Abstract In recent years, the word magma has been used to designate a pair of the form (S,∗) where * is a binary operation on the set S. Inspired by that terminology, we use the notation and terminology M(S) (the magma of S) to denote the set of all binary operations on the set S (i.e. the set of all magmas with underlying set S.) We study distributivity relations among magmas in the context of a hierarchy

Abstract Let R be a ring and n, k two non-negative integers. In this paper, we introduce the concepts of n-weak injective and n-weak flat modules and via the notion of special super finitely presented modules, we obtain some characterizations of these modules. We also investigate two classes of modules with richer contents, namely WIkn(R) and WFkn(Rop) which are larger than that of modules with weak

Abstract A subgroup H of a group G is contranormal if HG=G. In finite groups, if there are no proper contranormal subgroups, then the group is nilpotent but this is not true in infinite groups as the well-known Heineken–Mohamed groups show. We call such groups without proper contranormal subgroups “contranormal-free.” In this article, we prove various results concerning contranormal-free groups proving

Abstract We study the graph of zero-divisors of a quadratic quotient of a Rees algebra. We provide conditions in order to determine its girth and diameter, extending several results regarding amalgamated duplications and Nagata’s idealization.

Abstract The replacement property (or Steinitz Exchange Lemma) for vector spaces has a natural analog for finite groups and their generating sets. For the special case of the groups PSL(2,p), where p is a prime larger than 5, first partial results concerning the replacement property were published by Benjamin Nachman (2014 Nachman, B. (2014). Generating sequences of PSL(2,p). J. Group Theory 17(6):925–945

Abstract Let x¯=x1,…,xk denote an ordered sequence of elements of a commutative ring R. Let M be an R-module. We recall the two notions that x¯ is M-proregular given by Greenlees and May and Lipman and show that both notions are equivalent. As a main result we prove a cohomological characterization for x¯ to be M-proregular in terms of Čech cohomology. This implies also that x¯ is M-weakly proregular

Abstract The zero-divisor graphs of commutative rings have been used to build bridges between ring theory and graph theory. Namely, they have been used to characterize many ring properties in terms of graphic ones. However, many results are established only for reduced rings because a zero-divisor graph defined in the classical manner lacks the information on relationship between powers of zero-divisors

Abstract Good semigroups form a class of submonoids of Nd containing the value semigroups of curve singularities. In this article, we describe a partition of the complement of good semigroup ideals. As main application, we describe the Apéry sets of good semigroups with respect to arbitrary elements. This generalizes to any d≥2 the results in the study of D’Anna et al., which are proved in the case

Abstract The aim of this paper is to study quasitriangular structures on a class of semisimple Hopf algebras kG#σ,τkZ2 constructed through abelian extensions of kZ2 by kG for an abelian group G. We prove that there are only two forms of them and we get a complete list of all universal R-matrices of the generalized Kac-Paljutkin algebra H2n2 (see Section 2 for the definition).

Abstract In this paper, investigating the nonassociative version of groupoids and inverse semigroups, we study the relationship between these two algebraic structures and show that it can not be one-to-one.

Abstract A ring is called nil clean if every element can be written as the sum of an idempotent and a nilpotent. The class of nil clean rings has emerged as an important variant of the much-studied class of clean rings. However, the nil clean definition is fairly restrictive, and the collection of examples is rather constrained. In this paper, we propose an ideal-theoretic version of the nil clean