Showing papers in "Communications in Algebra in 2022"
TL;DR: In this paper , the transposed BiHom-Poisson (abbr. TBP) algebras which can be constructed by biHom-Novikov poisson (BP) was introduced.
Abstract: Abstract In this paper, we introduce the concept of transposed BiHom-Poisson (abbr. TBP) algebras which can be constructed by BiHom-Novikov-Poisson algebras. Several useful identities for TBP algebras are provided. We also prove that the tensor products of two (T)BP algebras are closed. The notions of BP 3-Lie algebras and TBP 3-Lie algebras are presented and TBP algebras can induce TBP 3-Lie algebras by two approaches. Finally, we give some examples for the TBP algebras of dimension 2.
9 citations
TL;DR: It is shown that the set of codegrees of and determines the group up to isomorphism.
Abstract: Abstract Let G be a finite group and The codegree of χ is defined as and is called the set of codegrees of G. In this paper, we show that the set of codegrees of and determines the group up to isomorphism.
8 citations
TL;DR: In this paper , a limit variety of monoid is defined as a monoid whose proper subvarieties are finitely based, and a variety of algebras is a limit monoid if it is non-finitely based.
Abstract: A variety of algebras is a limit variety if it is non-finitely based but all its proper subvarieties are finitely based. We present a new pair of limit varieties of monoids and show that together with the five limit varieties of monoids previously discovered by Jackson, Zhang and Luo and the first-named author, there are exactly seven limit varieties of J-trivial monoids.
6 citations
TL;DR: In this article , it was shown that the set of all tilting complexes over the block is isomorphic to the set over B as partially ordered sets, and that all the tilting complex over B is a tilting-discrete algebra.
Abstract: Abstract Let p be a prime number, k an algebraically closed field of characteristic p, a finite group, and G a normal subgroup of having a p-power index in . Moreover let B be a block of kG with a cyclic defect group and be the unique block of covering B. We study tilting complexes over the block and show that the block is a tilting-discrete algebra. Moreover we show that the set of all tilting complexes over is isomorphic to that over B as partially ordered sets.
5 citations
TL;DR: In this article , the authors extend Dade's theorem to the realm of nearly epsilon-strongly graded rings, and present new characterizations of strongly and epsilar strongly-grained rings.
Abstract: Abstract We extend Dade’s theorem to the realm of nearly epsilon-strongly graded rings, and present new characterizations of strongly and epsilon-strongly graded rings. Further, we give conditions for an epsilon-strongly graded ring to be written as a direct sum of strongly graded rings and a ring with trivial gradation. Our results are applied to characterize strongly graded Leavitt path algebras endowed with the canonical gradation. Finally we show that for any there is a Leavitt path algebra which is a sum of n − 1 strongly graded rings and a ring with trivial gradation.
5 citations
TL;DR: In this article , the authors give necessary and sufficient conditions on a and b so that p is a common index divisor of K. In particular, if any one of these conditions holds, then K is not monogenic.
Abstract: Abstract Let be a number field generated by a complex root α of a monic irreducible trinomial In this paper, for every prime integer p, we give necessary and sufficient conditions on a and b so that p is a common index divisor of K. In particular, if any one of these conditions holds, then K is not monogenic.
5 citations
TL;DR: In this paper , the set of all the ideals of a ring, endowed with the coarse lower topology, is considered and the aim is to study topological properties of distinguished subspaces of this space and detect the spectrality of some of them.
Abstract: Abstract We consider the set of all the ideals of a ring, endowed with the coarse lower topology. The aim of this paper is to study topological properties of distinguished subspaces of this space and detect the spectrality of some of them.
4 citations
TL;DR: In this paper , the concept of relative strongly Gorenstein flat modules is introduced, and a survey of their behavior in terms of both structural and dimension properties is given, including the stability of the GFL condition under iterations of its construction.
Abstract: Abstract In this article, the new concept of relative Gorenstein flat modules is introduced. We give a survey of their behavior in terms of both structural and dimension properties. We relate the class consisting of all these new modules to those of classical Gorenstein flat modules and of relative Gorenstein injective modules, and we compare the corresponding homological dimensions. This treatment includes the study of relative strongly Gorenstein flat modules as an important and structural part of relative Gorenstein flat modules. We also tackle the classical problem of the stability of the Gorenstein condition under iterations of its construction.
4 citations
TL;DR: In this article , the problem of the classification of indecomposable solutions of the Yang-Baxter equation was studied, using a scheme proposed by Bachiller, Cedó, and Jespers.
Abstract: Abstract In this paper we study the problem of the classification of indecomposable solutions of the Yang-Baxter equation. Using a scheme proposed by Bachiller, Cedó, and Jespers, and recent advances in the classification of braces we classify all indecomposable solutions with some particular permutation groups. We do this for all groups of size pq, all abelian groups of size p 2 q and all dihedral groups of size p 2 q.
4 citations
TL;DR: In this paper , the notion of commutator of ideals in a left skew brace is studied and the so-called (Huq = Smith) condition holds for left skew braces.
Abstract: Abstract We examine the pointed protomodular category SKB of left skew braces. We study the notion of commutator of ideals in a left skew brace. Notice that in the literature, “product” of ideals of skew braces is often considered. We show that the so-called (Huq = Smith) condition holds for left skew braces. Finally, we give a set of generators for the commutator of two ideals, and prove that every ideal of a left skew brace has a centralizer.
4 citations
TL;DR: In this paper , the arithmetic of monoids of zero-sum sequences over finite abelian groups is studied. But the focus was on zero-Sum constants rather than the arithmetic for the monoids formed by these sequences.
Abstract: Abstract The investigation of the arithmetic of monoids of zero-sum sequences over finite abelian groups is a classical subject due to their crucial role in understanding the arithmetic of (transfer) Krull monoids. More recently, sequences that admit, for a given set of weights, a weighted zero-sum received increased attention. Yet, the focus was on zero-sum constants rather than the arithmetic of the monoids formed by these sequences. We begin a systematic study of the arithmetic of these monoids. We show that for a wide class of weights unions of sets of lengths are intervals and we obtain various results on the elasticity of these monoids. More detailed results are obtained for the special case of plus-minus weighted sequences. Moreover, we apply our results to obtain results on factorizations of norms of algebraic integers.
TL;DR: In this article , the invariant bilinear form in a quadratic Lie-Yamaguti algebra induces an isomorphism between the adjoint representation and the coadjoint representation.
Abstract: In this paper, first we show that the invariant bilinear form in a quadratic Lie-Yamaguti algebra induces an isomorphism between the adjoint representation and the coadjoint representation. Then we introduce the notions of relative Rota-Baxter operators on Lie-Yamaguti algebras and pre-Lie-Yamaguti algebras. We prove that a pre-Lie-Yamaguti algebra gives rise to a Lie-Yamaguti algebra naturally and a relative Rota-Baxter operator induces a pre-Lie-Yamaguti algebra. Finally, we study symplectic structures on Lie-Yamaguti algebra, which give rise to relative Rota-Baxter operators as well as pre-Lie-Yamaguti algebras. As applications, we study phase spaces of Lie-Yamaguti algebras, and show that there is a one-to-one correspondence between phase spaces of Lie-Yamaguti algebras and Manin triples of pre-Lie-Yamaguti algebras.
TL;DR: In this paper , the additive structure of a positive real number has been studied in terms of the ascending chain condition on principal ideals in the setting of nonnegative integers. But the authors focus on the additive structures of real numbers.
Abstract: For a positive real number $\alpha$, let $\mathbb{N}_0[\alpha,\alpha^{-1}]$ be the semiring of all real numbers $f(\alpha)$ for $f(x)$ lying in $\mathbb{N}_0[x,x^{-1}]$, which is the semiring of all Laurent polynomials over the set of nonnegative integers $\mathbb{N}_0$. In this paper, we study various factorization properties of the additive structure of $\mathbb{N}_0[\alpha, \alpha^{-1}]$. We characterize when $\mathbb{N}_0[\alpha, \alpha^{-1}]$ is atomic. Then we characterize when $\mathbb{N}_0[\alpha, \alpha^{-1}]$ satisfies the ascending chain condition on principal ideals in terms of certain well-studied factorization properties. Finally, we characterize when $\mathbb{N}_0[\alpha, \alpha^{-1}]$ satisfies the unique factorization property and show that, when this is not the case, $\mathbb{N}_0[\alpha, \alpha^{-1}]$ has infinite elasticity.
DOI•
TL;DR: In this article , the concepts of arbitrary t-spread lexsegments and arbitrary t− spread lexsegment ideals with t a positive integer were introduced. And they were used to characterize all completely t−spread lex segment ideals.
Abstract: Abstract In this article we introduce the concepts of arbitrary t–spread lexsegments and of arbitrary t–spread lexsegment ideals with t a positive integer. These concepts are a natural generalization of arbitrary lexsegments and arbitrary lexsegment ideals. An ideal generated by an arbitrary t–spread lexsegment is called completely t–spread lexsegment if it is equal to the intersection of an initial t–spread lexsegment ideal and of a final t–spread lexsegment ideal. We study the class of arbitrary t–spread lexsegment ideals. In particular, we characterize all completely t–spread lexsegment ideals. Moreover, we classify all completely t–spread lexsegment ideals with a linear resolution.
TL;DR: In this paper , for any septic number field K generated by a root α of a monic irreducible trinomial, all prime power divisors of the index of K answering Problem 22 of Narkiewicz were described.
Abstract: Abstract In this paper, for any septic number field K generated by a root α of a monic irreducible trinomial , we describe all prime power divisors of the index of K answering Problem 22 of Narkiewicz [ 26]. In particular, if , then K is not mongenic. We illustrate our results by some computational examples.
TL;DR: In this article , it was shown that the core inverse and the pseudo core inverse can be characterized in terms of the w-core inverse of a given element, and the connections between the wcore inverse and other generalized inverses are given.
Abstract: Abstract Let S be a -semigroup and let . The initial goal of this work is to introduce two new classes of generalized inverses, called the w-core inverse and the dual v-core inverse in S. An element is w-core invertible if there exists some such that , xawa = a and . Such an x is called a w-core inverse of a. It is shown that the core inverse and the pseudo core inverse can be characterized in terms of the w-core inverse. Several characterizations of the w-core inverse of a are derived, and the expression is given by the inverse of w along a and {1, 3}-inverses of a in S. Also, the connections between the w-core inverse and other generalized inverses are given. In particular, when S is a -ring, the criterion for the w-core inverse is given by units. The dual v-core inverse of a is defined by the existence of satisfying , avay = a and . Dual results for the dual v-core inverse also hold. Communicated by Pace Nielsen
TL;DR: In this paper , the authors studied the Reidemeister spectrum of finitely generated torsion-free 2-step groups associated to graphs and developed three methods, based on the structure of the graph, that can be used to determine the this paper .
Abstract: ABSTRACT In this paper we study the Reidemeister spectrum of finitely generated torsion-free 2-step nilpotent groups associated to graphs. We develop three methods, based on the structure of the graph, that can be used to determine the Reidemeister spectrum of the associated group in terms of the Reidemeister spectra of groups associated to smaller graphs. We illustrate our methods for several families of graphs, including all the groups associated to a graph with at most four vertices. We also apply our results in the context of topological fixed point theory for nilmanifolds.
TL;DR: In this paper , it was shown that a cyclic extension of a simple group is an almost simple group, where the quotient of the solvable radical of the group is the same set of orders of elements.
Abstract: We say that finite groups are isospectral if they have the same sets of orders of elements. It is known that every nonsolvable finite group $G$ isospectral to a finite simple group has a unique nonabelian composition factor, that is, the quotient of $G$ by the solvable radical of $G$ is an almost simple group. The main goal of this paper is prove that this almost simple group is a cyclic extension of its socle. To this end, we consider a general situation when $G$ is an arbitrary group with unique nonabelian composition factor, not necessarily isospectral to a simple group, and study the prime graph of $G$, where the prime graph of $G$ is the graph whose vertices are the prime numbers dividing the order of $G$ and two such numbers $r$ and $s$ are adjacent if and only if $r
eq s$ and $G$ has an element of order $rs$. Namely, we establish some sufficient conditions for the prime graph of such a group to have a vertex adjacent to all other vertices. Besides proving the main result, this allows us to refine a recent result by P. Cameron and N. Maslova concerning finite groups almost recognizable by prime graph.
TL;DR: In this paper , it was shown that R is an Artinian Gorenstein ring if and only if every ideal in R is a trace ideal, and when the trace ideal of a module coincides with its double annihilator.
Abstract: Let R be a local Noetherian commutative ring. We prove that R is an Artinian Gorenstein ring if and only if every ideal in R is a trace ideal. We discuss when the trace ideal of a module coincides with its double annihilator.
TL;DR: In this article , a uniquely determined positive integer is associated with a valuation transcendental extension via a chosen minimal pair of definition, but it is later shown to be independent of the choice.
Abstract: An extension (K(X)|K, v) of valued fields is said to be valuation transcendental if we have equality in the Abhyankar inequality. Minimal pairs of definition are fundamental objects in the investigation of valuation transcendental extensions. In this article, we associate a uniquely determined positive integer with a valuation transcendental extension. This integer is defined via a chosen minimal pair of definition, but it is later shown to be independent of the choice. Further, we show that this integer encodes important information regarding the implicit constant field of the extension (K(X)|K, v).
TL;DR: In this paper , the authors construct new explicit examples of nonsmoothable Gorenstein algebras with Hilbert functions, which gives a new infinite family of elementary components in the Hilbert locus of points and solves the cubic case of Iarrobino's conjecture.
Abstract: Abstract We construct new explicit examples of nonsmoothable Gorenstein algebras with Hilbert function . This gives a new infinite family of elementary components in the Gorenstein locus of the Hilbert scheme of points and solves the cubic case of Iarrobino’s conjecture.
TL;DR: In this paper , an invariant of Cohen-Macaulay local rings in terms of the reduction number of canonical ideals is defined and the invariant can be defined in arbitrary Cohen-macaulay rings and it measures how close to being Gorenstein.
Abstract: In this article, we introduce an invariant of Cohen-Macaulay local rings in terms of the reduction number of canonical ideals. The invariant can be defined in arbitrary Cohen-Macaulay rings and it measures how close to being Gorenstein. First, we clarify the relation between almost Gorenstein rings and nearly Gorenstein rings by using the invariant in dimension one. We next characterize the idealization of trace ideals over Gorenstein rings in terms of the invariant. It provides better prospects for a result on the almost Gorenstein property of idealization.
TL;DR: In this paper , the monoid of all partial isometries of a star graph with n vertices is considered and the rank and cardinality of this monoid are determined. But the main objectives of the work are to determine the rank of the complete monoid and its cardinality.
Abstract: ABSTRACT In this paper we consider the monoid of all partial isometries of a star graph Sn with n vertices. Our main objectives are to determine the rank and to exhibit a presentation of . We also describe Green’s relations of and calculate its cardinal.
TL;DR: In this article , the authors introduced the notion of linear twisted vertices in the case where , and then established the uniqueness for such vertices under the conditions that either χ is an -lift for a π-chain of G or it has a linear Navarro vertex.
Abstract: Abstract Let G be a finite π-separable group, where π is a set of primes, and let χ be an irreducible complex character that is a π-lift of some π-partial character of G. It was proved by Cossey and Lewis that all of the vertex pairs for χ are linear and conjugate in G if , but the result can fail for . In this paper we introduce the notion of the linear twisted vertices in the case where , and then establish the uniqueness for such vertices under the conditions that either χ is an -lift for a π-chain of G or it has a linear Navarro vertex, thus answering a question proposed by them.
TL;DR: In this paper , the authors studied the set of radical semistar operations of an integral domain D and showed that their set is a complete lattice that is the join-completion of a set of spectral operations.
Abstract: Abstract We introduce and study the set of radical semistar operations of an integral domain D. We show that their set is a complete lattice that is the join-completion of the set of spectral semistar operations, and we characterize when every radical operation is spectral (under the hypothesis that D is rad-colon coherent). When D is a Prüfer domain such that every set of minimal prime ideals is scattered, we completely classify stable semistar operations.
TL;DR: In this article , the authors characterized the strong metric dimension of the commuting graph of a finite group and gave upper and lower bounds for the metric dimension for a dihedral group, a generalized quaternion group and a semidihedral group.
Abstract: ABSTRACT The commuting graph of a finite group is the undirected graph whose vertex set is the set of all elements of this group, and two distinct vertices are adjacent if they commute. In this paper, we characterize the strong metric dimension of the commuting graph of a finite group and give upper and lower bounds for the metric dimension of the commuting graph of a finite group. As applications, we compute the metric and strong metric dimension of the commuting graph of a dihedral group, a generalized quaternion group and a semidihedral group.
TL;DR: In this paper , the authors introduce general w-ZPI-rings, which are commutative rings where every proper w-ideal is a w-product of prime W-ideals.
Abstract: Abstract The w-operation, which is in some respects a “better behaved” variant of the classic t-operation, has recently been an object of intense study. In this article, we introduce and study general w-ZPI-rings, which are commutative rings where every proper w-ideal is a w-product of prime w-ideals. We give several characterizations of general w-ZPI-rings and investigate when a monoid ring with S cancellative is a general w-ZPI-ring. On the way to answering the latter question, we formulate a reusable tool for reducing certain monoid ring classification problems to the monoid domain special case.
TL;DR: In this paper , the authors investigated the class groups and distribution of prime divisors in affine monoid algebras over fields and thereby extend the result of Kainrath that every finitely generated integral algebra of Krull dimension at least 2 over an infinite field has infinitely many prime diviators in all classes.
Abstract: We investigate the class groups and the distribution of prime divisors in affine monoid algebras over fields and thereby extend the result of Kainrath that every finitely generated integral algebra of Krull dimension at least 2 over an infinite field has infinitely many prime divisors in all classes.
TL;DR: In this paper , it was shown that any stack X of finite type over a Noetherian scheme has a presentation X→X by a scheme of finite-type such that X(F)→X (F) is onto, for every finite or real closed field F. Under some additional conditions on X, they showed the same for all perfect fields.
Abstract: We show that any stack X of finite type over a Noetherian scheme has a presentation X→X by a scheme of finite type such that X(F)→X(F) is onto, for every finite or real closed field F. Under some additional conditions on X, we show the same for all perfect fields. We prove similar results for (some) Henselian rings. We give two applications of the main result. One is to counting isomorphism classes of stacks over the rings Z/pn; the other is about the relation between real algebraic and Nash stacks.
TL;DR: In this article , the authors established necessary or sufficient conditions for skew Poincaré-Birkhoff-Witt extensions of noncommutative rings such as universal enveloping algebras and differential operators.
Abstract: We establish necessary or sufficient conditions to guarantee that skew Poincaré–Birkhoff–Witt extensions are NI or NJ rings. Our results extend those corresponding for skew polynomial rings and establish similar properties for other families of noncommutative rings such as universal enveloping algebras and examples of differential operators.