Showing papers in "Communications in Algebra in 2021"
TL;DR: In this article, the minimum degree, indescrete power graph Pe(G) of a group G is a graph with vertex set G and two vertices are adjacent if they belong to the same cyclic subgroup.
Abstract: The enhanced power graph Pe(G) of a group G is a graph with vertex set G and two vertices are adjacent if they belong to the same cyclic subgroup. In this paper, we consider the minimum degree, ind...
22 citations
TL;DR: The atomic structure of Puiseux algebras has been studied in this paper, where it is shown that if two Puiseaux algebraic monoids are isomorphic, then the monoids must be isomorphic.
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 $\mathbb{Q}_{\ge 0}$ 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 $F[M_1]$ and $F[M_2]$ are isomorphic, then the monoids $M_1$ and $M_2$ must be isomorphic. Then we construct three classes of Puiseux algebras satisfying the following well-known atomic properties: the ACCP property, the bounded factorization property, and the finite factorization property. We show that there are bounded factorization Puiseux algebras with extremal systems of sets of lengths, which allows us to prove that Puiseux algebras cannot be determined up to isomorphism by their arithmetic of lengths. Finally, we give a full description of the seminormal closure, root closure, and complete integral closure of a Puiseux algebra, and use such description to provide a class of antimatter Puiseux algebras (i.e., Puiseux algebras containing no irreducibles).
16 citations
TL;DR: In this article, the complex type k-Fibonacci numbers were defined and the relationship between the k-step Fibonacci number and the complex-type k-fibonach number was investigated.
Abstract: In this article, we define the complex-type k-Fibonacci numbers and then give the relationships between the k-step Fibonacci numbers and the complex-type k-Fibonacci numbers. Also, we obtain miscel...
15 citations
TL;DR: A dendriform algebra is an associative algebra whose product splits into two binary operations and the associativity splits into three new identities as mentioned in this paper, where the product can be expressed as a binary operation.
Abstract: A dendriform algebra is an associative algebra whose product splits into two binary operations and the associativity splits into three new identities. These algebras arise naturally from some combi...
15 citations
TL;DR: In this paper, a monic irreducible polynomial F(x)=x2r·5s−m, with m≠∓1 is a square free integer, r and s are two positive integers.
Abstract: Let K=Q(α) be a pure number field generated by a root α of a monic irreducible polynomial F(x)=x2r·5s−m, with m≠∓1 is a square free integer, r and s are two positive integers. In this article, we s...
14 citations
TL;DR: The Positivstellensatz theorem on preordered commutative semirings satisfying a boundedness condition similar to Archimedeanicity was introduced in this article.
Abstract: Strassen’s Positivstellensatz is a powerful but little known theorem on preordered commutative semirings satisfying a boundedness condition similar to Archimedeanicity. It characterizes the relaxed...
13 citations
TL;DR: In this paper, minimal algebraic surfaces of general type with K 2 = 3pg−5 were studied. And they proved that for the case of K 2 ≥ 3, there is no polynomial-time algebraic algebraic surface with k 2 = 2.
Abstract: In this paper, we study minimal algebraic surfaces of general type with K2=3pg−5. Since the case pg≤4 has been studied by Horikawa, Zucconi, and Bauer, we always assume pg≥5 here. We prove that for...
13 citations
TL;DR: In this article, the authors define the no-no relation between prime and primary hyperideals in a Krasner (m, n)-hyperring and define a no-No relation between the two structures.
Abstract: Prime hyperideals and primary hyperideals as two of the most important structures in a Krasner (m, n)-hyperring are defferent from each other in many aspects. In this paper, we aim to define the no...
13 citations
TL;DR: In this article, the weak and the ( X, Y ) -Gorenstein relative projective objects in an abelian category were defined, where X and Y are two classes of objects in A.
Abstract: Let A be an abelian category. For a pair ( X , Y ) of classes of objects in A , we define the weak and the ( X , Y ) -Gorenstein relative projective objects in A . We point out that such objects ge...
12 citations
TL;DR: In this article, the cohomology and deformation theory of 3-Lie algebras is revisited and the theory of extending structures and unified product for 3-lie algesbras are developed.
Abstract: The cohomology and deformation theory of 3-Lie algebras are revisited. The theory of extending structures and unified product for 3-Lie algebras are developed. It is proved that the extending struc...
12 citations
TL;DR: In this paper, the φ function for cyclic Nakayama algebras of infinite global dimension was studied, and the behavior of φ functions was shown to be invariant to the number of vertices.
Abstract: Igusa and Todorov introduced the φ function which generalizes the notion of projective dimension. We study the behavior of the φ function for cyclic Nakayama algebras of infinite global dimension. ...
TL;DR: In this paper, a commutative ring with unit element is considered, and the R -algebra G = G (A, M, N, B ) is a generalized matrix algebras.
Abstract: Let R be a commutative ring with unit element, A , B be R -algebras, M be an ( A , B ) -bimodule, and N be a ( B , A ) -bimodule. The R -algebra G = G ( A , M , N , B ) is a generalized matrix alge...
TL;DR: In this article, minimal cut-sets of the power graph of a finite non-cyclic nilpotent group which are associated with its maximal cyclic subgroups are studied.
Abstract: We study minimal cut-sets of the power graph of a finite non-cyclic nilpotent group which are associated with its maximal cyclic subgroups. As a result, we find the vertex connectivity of the power...
TL;DR: In this paper, the classes of free and plus-one generated hyperplane arrangements were studied and the associated prime ideals of the Jacobian ideal of such an arrangement were derived from the free hyperplane arrangement.
Abstract: We study the classes of free and plus-one generated hyperplane arrangements. Specifically, we describe how to compute the associated prime ideals of the Jacobian ideal of such an arrangement from i...
TL;DR: In this article, a family of complexes called trimming complexes is proposed and used to deduce the Betti table for the minimal free resolution problem. But the complexity of trimming complex is not fixed.
Abstract: We produce a family of complexes called trimming complexes and explore its applications. We demonstrate how trimming complexes can be used to deduce the Betti table for the minimal free resolution ...
TL;DR: In this article, it was shown that if a nonsolvable group G has exactly five characters codegrree, then the codegree of group G is defined as |G:ker(χ)|/χ(1).
Abstract: Let G be a finite group and the codegree of irreducible character χ of group G is defined as |G:ker(χ)|/χ(1). In this paper, we prove that if a nonsolvable group G has exactly five character codegr...
TL;DR: In this article, it was shown that if |G | = n and ψ (G ) > 13 21 ψ(C n ), then G is a cyclic group of order n.
Abstract: Denote the sum of element orders in a finite group G by ψ ( G ) and let Cn denote the cyclic group of order n. In this paper, we prove that if | G | = n and ψ ( G ) > 13 21 ψ ( C n ) , then G is ni...
TL;DR: An ideal P of R with P ∩ S = ∅ is called an S-prime ideal if there exists an (fixed) s ∈ S and when... as discussed by the authors.
Abstract: Let R be a commutative ring with nonzero identity and, S ⊆ R be a multiplicatively closed subset. An ideal P of R with P ∩ S = ∅ is called an S-prime ideal if there exists an (fixed) s ∈ S and when...
TL;DR: In this article, the notion of isoclinism on central extensions of Lie superalgebras was studied and conditions under which central extensions are isocliic were discussed.
Abstract: We study the notion of isoclinism on central extensions of Lie superalgebras and discuss some conditions under which central extensions are isoclinic as well as some results on isoclinic homomorphi...
TL;DR: In this article, the classifying space of τ-cluster morphism categories was shown to be the same as the space of cluster morphism classes defined by Igusa and Todorov.
Abstract: τ-cluster morphism categories, introduced by Buan and Marsh, are a generalization of cluster morphism categories (defined by Igusa and Todorov). We show the classifying space of such a category is ...
TL;DR: In this article, the atomic properties of exponential Puiseux monoid and semiring monoid were studied and shown to be linear in the number of powers of a rational number in the monoid.
Abstract: We say that a Puiseux monoid is exponential provided that it is generated by some of the powers of a rational number. Here we study the atomic properties of exponential Puiseux monoids and semiring...
TL;DR: In this article, it was shown that distributive law holds for non-abelian tensor product of Lie superalgebras under certain direct sums, and a distributive rule for nonabelian exterior square of a Lie super-algebra is given.
Abstract: In this article, we show that distributive law holds for non-abelian tensor product of Lie superalgebras under certain direct sums. Thereby we obtain a rule for non-abelian exterior square of a Lie...
TL;DR: The Reidemeister number of equivalence classes for φ-conjugate endomorphisms is the largest known for any relation in the Reid-Meister number as mentioned in this paper.
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 ...
TL;DR: In this paper, the authors propose a promising platform for implementation of protocols of Diffie-Hellman and Stickel type based on the CSR expansi cation, which has been recently put forward by Grigoriev and Shpilrain.
Abstract: Tropical linear algebra has been recently put forward by Grigoriev and Shpilrain as a promising platform for implementation of protocols of Diffie-Hellman and Stickel type. Based on the CSR expansi...
TL;DR: In this paper, the connections between von Neumann regularity of endomorphisms and perspectivity of direct summands in modules are investigated, leading to a new classification of those rings whose regular elements...
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 ...
TL;DR: In this paper, it was proved that all 2-local superderivations on the super Virasoro algebra and the super W(2,2) algebra can be found.
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 al...
TL;DR: The algebraic formula is based on explicitly calculating the integrations of certain Chern classes of the universal bundles over the Grassmannians and generalizes the formula of the Chern–Mather class of in [18, theorem 10] to arbitrary algebraically closed base field.
Abstract: The local Euler obstructions are key ingredients in the study of both singularity theory and geometric representation theory. In this note, we consider matrix rank stratification over algebraically...
TL;DR: In this article, the authors consider a noncommutative prime ring with extended centroid C and maximal right ring of quotients Q, and give a generalized derivation of R.
Abstract: Let R be a noncommutative prime ring with extended centroid C and maximal right ring of quotients Q. Let I be a nonzero ideal of R, and let g, h be two generalized derivations of R. Suppose that [ ...
TL;DR: In this paper, the rational functions of degree three that permute the projective line P1(Fq) over a finite field Fq were determined by Ferraguti and Micheli.
Abstract: Recently, rational functions of degree three that permute the projective line P1(Fq) over a finite field Fq were determined by Ferraguti and Micheli. In the present paper, using a different method,...
TL;DR: In this paper, the authors show how to embed the hypoplactic monoid of any rank strictly greater than 2 (including infinite rank) into a direct product of copies of the Hypoplactic Monoid of rank 2.
Abstract: This paper presents new results on the identities satisfied by the hypoplactic monoid. We show how to embed the hypoplactic monoid of any rank strictly greater than 2 (including infinite rank) into a direct product of copies of the hypoplactic monoid of rank 2. This confirms that all hypoplactic monoids of rank greater than or equal to 2 satisfy exactly the same identities. We then give a complete characterization of those identities, and prove that the variety generated by the hypoplactic monoid has finite axiomatic rank, by giving a finite basis for it.