Showing papers in "Communications in Algebra in 2019"
TL;DR: In this paper, the classification of all n-dimensional anticommutative complex algebras with (n − − 3)-dimensional annihilator is given, and all central extensions of all 3-dimensional acyclic complexes are described.
Abstract: We give the classification of all n-dimensional anticommutative complex algebras with (n − 3)-dimensional annihilator. Namely, we describe all central extensions of all 3-dimensional anticommutativ...
39 citations
TL;DR: In this paper, a new and natural topology on the prime spectrum is introduced, called the flat topology, which behaves completely as the dual of the Zariski topology.
Abstract: In this article, a new and natural topology on the prime spectrum is introduced, which behaves completely as the dual of the Zariski topology. It is called the flat topology. The basic and also som...
38 citations
TL;DR: In this article, the Castelnuovo-Mumford regularity of S/JG when JG is a binomial edge ideal is computed for simple graphs on n vertices.
Abstract: Let G be a finite simple graph on n vertices and JG denote the corresponding binomial edge ideal in S=K[x1,…,xn,y1,…,yn]. We compute the Castelnuovo-Mumford regularity of S/JG when JG is th...
32 citations
TL;DR: T-spread monomials and t-spread strongly stable ideals as discussed by the authors are a natural generalization of strongly stable and square-free strongly stable ideal ideals, and they have been shown to be useful in many problems.
Abstract: We introduce the concept of t-spread monomials and t-spread strongly stable ideals. These concepts are a natural generalization of strongly stable and squarefree strongly stable ideals. For the stu...
30 citations
TL;DR: In this paper, the authors use extensions of tropical algebras as platforms for very efficient public key exchange protocols, and they show that such extensions can be used for a wide range of applications.
Abstract: We use extensions of tropical algebras as platforms for very efficient public key exchange protocols.
27 citations
TL;DR: This article gives a characterization of finite groups with at most three codegrees of irreducible characters with a number of characters called χ.
Abstract: For a character χ of a finite group G, the number cod(χ)=|G:Ker(χ)|/χ(1) is called the codegree of χ. We also define cod(G)={cod(χ)∣χ∈Irr(G)}. In this article, we give a characterization of finite ...
25 citations
TL;DR: In this article, a p-adic analog of Kunz's theorem was proved: a padically complete noetherian ring is regular when it admits a faithfully flat map to a perfectoid ring.
Abstract: We prove a p-adic analog of Kunz’s theorem: a p-adically complete noetherian ring is regular exactly when it admits a faithfully flat map to a perfectoid ring. This result is deduced from a...
24 citations
TL;DR: In this article, it was shown that if k is a positive integer, then Ck denotes a cyclic group of order k and ψ(Ck) is the sum of orders of all elements of k.
Abstract: If G is a finite group, then ψ(G) denotes the sum of orders of all elements of G and if k is a positive integer, then Ck denotes a cyclic group of order k. Moreover, ψ(Ck) will be sometimes denoted...
23 citations
TL;DR: In this paper, the power graph of a finite group is defined as the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other.
Abstract: The power graph of a finite group is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other. In this article, we classify the finite gr...
23 citations
TL;DR: In this article, conditions on the Koszul complex of a noetherian local ring R guarantee that ToriR(M,N) is nonzero for infinitely many i, when M and N are finitely generated R-modules of infinite projective dimension.
Abstract: Conditions on the Koszul complex of a noetherian local ring R guarantee that ToriR(M,N) is nonzero for infinitely many i, when M and N are finitely generated R-modules of infinite projective dimension. These conditions are obtained from results concerning Tor of differential graded modules over certain trivial extensions of commutative differential graded algebras.Dedicated to Gennady Lyubeznik on the occasion of his 60th birthday.
22 citations
TL;DR: In this article, the Hilbert series of binomain ideal edges is computed for a simple graph on n vertices and the corresponding binomial edge ideal in the polynomial ring S = K.
Abstract: Let G be a finite simple graph on n vertices and JG denote the corresponding binomial edge ideal in the polynomial ring S=K[x1,…,xn,y1,…,yn]. In this article, we compute the Hilbert series of binom...
TL;DR: In this article, the n-step Lucas polynomials and their relationship are analyzed using two matrices, and the authors extend the study to the n step Lucas poynomials.
Abstract: In this article, we find elements of the Lucas polynomials by using two matrices. We extend the study to the n-step Lucas polynomials. Then the Lucas polynomials and their relationship are ...
TL;DR: In this paper, all groups are finite, and the symbol σ(n) denotes the set {σi|σi∩π(n)-≠∅}; σ (G)=σ(|G|) and σ((G, F)) = ∪ ∅.
Abstract: Throughout this paper, all groups are finite. Let σ={σi|i∈I} be some partition of the set of all primes P. If n is an integer, the symbol σ(n) denotes the set {σi|σi∩π(n)≠∅}; σ(G)=σ(|G|) and σ(F)=∪...
TL;DR: In this article, it was shown that all finite dimensional special Heisenberg Lie superalgebras with even center have dimension (2m+1|n) for some non-negative integers m, n and are isomorphic to H...
Abstract: In this article, first we prove that all finite dimensional special Heisenberg Lie superalgebras with even center have dimension (2m+1|n) for some non-negative integers m, n and are isomorphic to H...
TL;DR: A ring R with center C is said to be centrally essential if the module RC is an essential extension of the module CC as discussed by the authors, where R is defined as an extension of CC.
Abstract: A ring R with center C is said to be centrally essential if the module RC is an essential extension of the module CC. We describe centrally essential exterior algebras of finitely generated free mo...
TL;DR: In this paper, the theory of skew Armendariz and quasi-Armendariz modules over skew PBW extensions is developed, which generalizes the results of several works in the literature concerning skew armendariz.
Abstract: The aim of this article is to develop the theory of skew Armendariz and quasi-Armendariz modules over skew PBW extensions. We generalize the results of several works in the literature concerning th...
TL;DR: In this paper, the incidence algebra of a 2-torsion free commutative ring with unity and a locally finite preordered set has been studied, where X consists of a finite number of connected components and I(X,R) is the algebra of X over R.
Abstract: Let R be a 2-torsion free commutative ring with unity, X a locally finite preordered set and I(X,R) the incidence algebra of X over R. If X consists of a finite number of connected components, we p...
TL;DR: In this article, the authors investigated the Cohen-Macaulayness and algebraic invariants of the toric ring k[G] via the projective dimension of a simple graph.
Abstract: Let G=(V,E) be a simple graph. We investigate the Cohen–Macaulayness and algebraic invariants, such as the Castelnuovo-Mumford regularity and the projective dimension, of the toric ring k[G] via th...
TL;DR: In this article, it was shown that polynomial rings generated by a fixed number of homogeneous polynomials of fixed degrees have a finite number of possible generic initial ideals, independent of the number of variables that they involve and independently of the characteristic of the ground field.
Abstract: Using recent work by Erman–Sam–Snowden, we show that finitely generated ideals in the ring of bounded-degree formal power series in infinitely many variables have finitely generated Grobner bases relative to the graded reverse lexicographic order. We then combine this result with the first author’s work on topological Noetherianity of polynomial functors to give an algorithmic proof of the following statement: ideals in polynomial rings generated by a fixed number of homogeneous polynomials of fixed degrees only have a finite number of possible generic initial ideals, independently of the number of variables that they involve and independently of the characteristic of the ground field. Our algorithm outputs not only a finite list of possible generic initial ideals, but also finite descriptions of the corresponding strata in the space of coefficients. Dedicated to Gennady Lyubeznik on the occasion of his 60th birthday.
TL;DR: In this paper, the authors focus on how some graph operations affect the strong persistence property of an ideal I in a commutative Noetherian ring R in the sense that it has strong persistence if (It+1:RI) for all positive integers t.
Abstract: An ideal I in a commutative Noetherian ring R has the strong persistence property if (It+1:RI)=It for all positive integers t. In this article, we focus on how some graph operations affect the stro...
TL;DR: In this article, the authors investigated to what extent the directed (resp. undirected) reduced power graph determines the directed power graph (referred to as reduced power graphs).
Abstract: In this paper, for a finite group, we investigate to what extent its directed (resp. undirected) reduced power graph determines its directed power graph (resp. reduced power graph). Moreover, we in...
TL;DR: All Lie algebras such that there exists a post-Lie algebra structure on with .
Abstract: Rota–Baxter operators R of weight 1 on n are in bijective correspondence to post-Lie algebra structures on pairs (g,n), where n is complete. We use such Rota–Baxter operators to study the existence...
TL;DR: In this article, a notion of cellular automata over schemes which generalize affine algebraic cellular a... is introduced, based on the seminal work of Gromov on endomorphisms of symbolic algebraic varieties.
Abstract: Building on the seminal work of Gromov on endomorphisms of symbolic algebraic varieties, we introduce a notion of cellular automata over schemes which generalize affine algebraic cellular a...
TL;DR: The Cayley-Bacharach Property (CBP) was extended to arbitrary 0-dimensional affine algebras in this article, which is a property of a finite set of points in an affine or projective space.
Abstract: The Cayley-Bacharach Property (CBP), which has been classically stated as a property of a finite set of points in an affine or projective space, is extended to arbitrary 0-dimensional affine algebr...
TL;DR: In this paper, Fang, Li, and Xu proved that either G is normal in the full automorphism G-regular graph or G-simple group G is not normal.
Abstract: Let G be a finite non-abelian simple group and let Γ be a connected tetravalent 2-arc-transitive G-regular graph. In 2004, Fang, Li, and Xu proved that either G is normal in the full automorphism g...
TL;DR: In this article, many problems connected with finiteness properties of local cohomology modules, e.g., the associated primes, the minimal primes and Bass numbers, are discussed.
Abstract: This manuscript discusses many problems connected with finiteness properties of local cohomology modules, e.g. the associated primes, the minimal primes, Bass numbers, as well as the behavi...
TL;DR: In this article, conjectured generalizations of a formula of Lech which relates the multiplicity of a finite colength ideal in an equicharacteristic local ring to its colength were studied.
Abstract: We study conjectured generalizations of a formula of Lech which relates the multiplicity of a finite colength ideal in an equicharacteristic local ring to its colength and prove one of these genera...
TL;DR: In this article, the taxonomy of 2-primal rings is given, and examples of various types of rings that are related to commutativity such as reduced, symmetric, duo, reversible and PS I are given.
Abstract: In a paper on the taxonomy of 2-primal rings, examples of various types of rings that are related to commutativity such as reduced, symmetric, duo, reversible and PS I were given in order t...
TL;DR: The existence of a linear order on a group that is compatible with the group structure generally requires transfinite methods as mentioned in this paper, and this can be circumvented by concentrating on the cons.
Abstract: The existence of a linear order on a group that is compatible with the group structure generally requires transfinite methods. However, this can be circumvented by concentrating on the cons...
TL;DR: In this article, the class of dual-square-free (DSF) modules is defined, and the class is closed under direct summands and homomorphic images, and a modu...
Abstract: A module M is called dual-square-free (DSF) if M has no proper submodules A and B with M=A+B and M/A≅M/B. The class of DSF-modules is closed under direct summands and homomorphic images, and a modu...