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  • Graded powerful ideals in a graded integral domain
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-15
    Chahrazade Bakkari; Najib Mahdou; Abdelkbir Riffi

    Abstract In this paper, we introduce and study a generalization of powerful ideals, in the sense of Badawi and Houston, to the context of integral domains graded by a torsionless monoid.

    更新日期:2021-01-15
  • Cohn-Leavitt path algebras of bi-separated graphs
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-12
    R. Mohan; B. N. Suhas

    Abstract The purpose of this article is to provide a common framework for studying various generalizations of Leavitt path algebras. We first define Cohn-Leavitt path algebras of graphs with an additional structure called bi-separated graphs. We then define and study the category BSG of bi-separated graphs with appropriate morphisms so that the functor which associates bi-separated graphs to their

    更新日期:2021-01-12
  • On the amenability profile of infinite dimensional algebras
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-11
    Sergio R. López-Permouth; Benjamin Stanley

    Abstract Given a module T over an F-algebra A , and a basis B for T , the amenability domain of B is the subalgebra of A consisting of all elements r ∈ A with row finite matrix representation [ l r ] B with respect to B . A basis B of T having amenability domain equal to A is said to be an amenable basis. When an amenable basis for T exists, T is said to be an amenable module. A basis having amenability

    更新日期:2021-01-12
  • A note on outer derivations of Leibniz algebras
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-11
    G. R. Biyogmam; C. Tcheka

    Abstract In this article, we discuss completeness of non-Lie Leibniz algebras by studying various conditions under which they admit outer derivations. Our study focusses particularly on the class of non-perfect Leibniz algebras whose center is not contained in the Leibniz kernel. We extend to this class of Leibniz algebras several well-known results on derivations of Lie algebras. In particular, we

    更新日期:2021-01-12
  • Noncommutative differential calculus on (co)homology of hom-associative algebras
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-11
    Apurba Das

    Abstract A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. It was previously shown by the author that the Hochschild cohomology of a hom-associative algebra A carries a Gerstenhaber structure. In this short paper, we show that this Gerstenhaber structure together with certain operations on the Hochschild homology of A makes a noncommutative differential

    更新日期:2021-01-11
  • On a criterion for solvability of a finite group
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-10
    Marcel Herzog; Patrizia Longobardi; Mercede Maj

    Abstract Let G be a finite group and σ 1 ( G ) = 1 | G | ∑ H ≤ G | H | . Answering to a problem posed by M. Tărnăuceanu, we prove that, if σ 1 ( G ) < 117 20 , then G is solvable.

    更新日期:2021-01-11
  • On rigid 2-step nilpotent Lie superalgebras
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-08
    María Alejandra Alvarez; Yerko Anza

    Abstract The aim of this work is to provide a criterion for the rigidity of 2-step nilpotent Lie superalgebras in the variety N ( m | n ) 2 of 2-step nilpotent Lie superalgebras of dimension ( m | n ) . We give several examples of rigid 2-step nilpotent Lie superalgebras of any dimension.

    更新日期:2021-01-10
  • L-homologies of double complexes
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-08
    Amartya Goswami

    Abstract The notion of L-homologies (of double complexes) as proposed in this paper extends the notion of classical horizontal and vertical homologies along with two other new homologies introduced in the homological diagram lemma called the salamander lemma. We enumerate all L-homologies associated with an object of a double complex and provide new examples of exact sequences. We describe a classification

    更新日期:2021-01-08
  • The Grothendieck rings of Wu-Liu-Ding algebras and their Casimir numbers (II)
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-07
    Ruifang Yang; Shilin Yang

    Abstract Wu-Liu-Ding algebras, that is D ( m , d , ξ ) , are a class of non-pointed affine prime regular Hopf algebras of GK-dimension one. In this paper, we mainly study a class of quotient algebras of D ( m , d , ξ ) , denoted by D ′ ( m , d , ξ ) , which are 2 m 2 d -dimensional non-pointed semisimple Hopf algebras. For a better understanding of the structure of the Hopf algebra D ′ ( m , d , ξ

    更新日期:2021-01-07
  • Generalizations of Nagata’s theorem
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-07
    Ahmed Hamed; Walid Maaref; Omid Khani-Nasab

    Abstract Let D be an integral domain and S a multiplicative subset of D. According to the study of Hamed and Hizem, the S-class group of D, denoted by S- C l t ( D ) , is the group of fractional t-invertible t-ideals of D under the t-multiplication modulo its subgroup of S-principal t-invertible t-ideals of D. In this paper we study the case of isomorphism S- C l t ( D ) ≃  S- C l t ( D T ) , where

    更新日期:2021-01-07
  • Finding supercharacter theories on character tables
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-06
    Frieder Ladisch

    Abstract We describe an easy way how to find supercharacter theories for a finite group, if its character table is known. Namely, we show how an arbitrary partition of the conjugacy classes or of the irreducible characters can be refined to the coarsest partition that belongs to a supercharacter theory. Our constructions emphasize the duality between superclasses and supercharacters. An algorithm is

    更新日期:2021-01-06
  • Unique factorization of ideals in commutative rings with zero divisors
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-06
    J. R. Juett; Christopher Park Mooney; Lois W. Ndungu

    Abstract “Unique factorization” was central to the initial development of ideal theory. We update this topic with several new results concerning notions of “unique ideal factorization rings” with zero divisors. Along the way, we obtain new characterizations of several well-known kinds of rings in terms of their ideal factorization properties and examine when monoid rings satisfy various kinds of “unique

    更新日期:2021-01-06
  • Irreducible jet modules for the vector field Lie algebra on S 1 × C
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-06
    Mengnan Niu; Genqiang Liu

    Abstract For a commutative algebra A over C , denote g = Der ( A ) . A module over the smash product A # U ( g ) is called a jet g -module, where U ( g ) is the universal enveloping algebra of g . In the present paper, we study jet modules in the case of A = C [ t 1 ± 1 , t 2 ] . We show that A # U ( g ) ≅ D ⊗ U ( L ) , where D is the Weyl algebra C [ t 1 ± 1 , t 2 , ∂ ∂ t 1 , ∂ ∂ t 2 ] , and L is

    更新日期:2021-01-06
  • Maximal subgroup growth of some metabelian groups
    Commun. Algebra (IF 0.556) Pub Date : 2021-01-02
    Andrew James Kelley

    Abstract Let G be a finitely generated group, and let m n ( G ) denote the number of maximal subgroups of G of index n. An upper bound is given for the degree of maximal subgroup growth of all polycyclic metabelian groups G (i.e., for lim sup   log   m n ( G )   log   n , the degree of polynomial growth of m n ( G ) ). A condition is given for when this upper bound is attained. Let G = Z k ⋊ A Z ,

    更新日期:2021-01-02
  • Complete Bihom-Lie superalgebras and its derivation superalgebras
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-30
    Yusi Fan; Juan Li; Liangyun Chen

    Abstract This paper aims to research some basic results on complete Bihom-Lie superalgebras. Particularly, we give some sufficient conditions for a Bihom-Lie superalgebra to be complete. Afterwards, we determine explicitly the derivation superalgebras of centerless perfect Bihom-Lie superalgebras of arbitrary dimension and characteristic over any field are complete. Meanwhile some related properties

    更新日期:2020-12-30
  • Derived invariants for surface cut algebras of global dimension 2 II: the punctured case
    Commun. Algebra (IF 0.556) Pub Date : 2020-11-21
    Claire Amiot; Daniel Labardini-Fragoso; Pierre-Guy Plamondon

    Abstract For algebras of global dimension 2 arising from a cut of the quiver with potential associated with a triangulation of an unpunctured surface, Amiot-Grimeland defined integer-valued functions on the first homology groups of the surfaces. Derived equivalences translate to the existence of automorphisms of surfaces preserving these functions. We generalize this to punctured surfaces. Moreover

    更新日期:2020-12-29
  • The representation invariants of 2-term silting complexes
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-29
    Yonggang Hu

    Abstract Let A be a finite dimensional k-algebra and P a 2-term silting complex in K b ( proj A ) . In this article, we investigate the representation dimension of End D b ( A ) ( P ) by the silting theory. We show that if P is a separating silting complex with certain homological restriction, then, rep.dim A = rep.dim End D b ( A ) ( P ) . This result generalizes the earlier result about tilting modules

    更新日期:2020-12-29
  • Menger hyperalgebras and their representations
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-29
    Thodsaporn Kumduang; Sorasak Leeratanavalee

    Abstract The paper is devoted to the investigation of algebraic hyperstructures. The concept of Menger hyperalgebras, which is a canonical generalization of semihypergroups, is introduced. The emphasis of this paper is on the algebraic nature of such structure concerning subhyperalgebras, homomorphisms and quotient hyperstructures, that allows for a rich algebraic theory. Based on the theory of multiplace

    更新日期:2020-12-29
  • Semi-invariants of low-dimensional Lie algebras
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-28
    M. A. Alvarez; G. Salgado

    Abstract The aim of this work is to explicitly compute the semi-invariants of low-dimensional Lie algebras by reducing the amount of work, i.e., we can prove that almost every irreducible Lie algebra g , of dimension less than or equal to 5, satisfies the following: It is either a contact Lie algebra or there exists a torus T ⊂ Der ( g ) such that T   ⋉ g is a contact Lie algebra. Therefore, the semi-invariants

    更新日期:2020-12-28
  • The divided, going-down, and Gaussian properties of amalgamation of rings
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-25
    Najib Mahdou; Sanae Moussaoui; Siamak Yassemi

    Abstract We provide necessary and sufficient conditions for the amalgamation of rings A ⋈ f J to be a divided ring, locally divided ring, going-down ring, and Gaussian ring.

    更新日期:2020-12-26
  • Associates, irreducibility, and factorization length in monoid rings with zero divisors
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-25
    Ranthony A. C. Edmonds; J. R. Juett

    Abstract In the context of factorization in monoid rings with zero divisors, we study associate relations and the resulting notions of irreducibility and factorization length. Building upon these facts, we determine necessary and sufficient conditions for broad classes of monoid rings to satisfy the ascending chain condition on principal ideals or be a bounded factorization ring. Along the way, we

    更新日期:2020-12-26
  • More on rank-2 tori and its cohomological applications
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-24
    Neha Hooda

    Abstract Let k be a field of characteristic different from 2 and 3. In this paper, we study the maximal k-tori T in the connected simple algebraic groups of type A 2 and G 2. We refer to these tori as unitary tori. We study the cohomology H 1 ( k , T ) and deduce how the presence of maximal k-tori with H 1 ( k , T ) = 0 effects the structure of these groups.

    更新日期:2020-12-25
  • On linearly chinese field extensions
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-22
    Cornelius Greither; Lucas Reis

    Abstract Given a collection A = { L 1 , … , L n } of intermediate fields in a field extension L/K of finite degree and Λ L , A = L 1 × ⋯ × L n , there is a natural map Ψ L , A : L → Λ L , A given by y ↦ ( Tr L / L 1 ( y ) , … , Tr L / L n ( y ) ) , where Tr L / L i : L → L i denotes the trace. The image set Ψ L , A ( L ) turns out to be contained in a certain subset Λ L , A * of Λ L , A (in fact, a

    更新日期:2020-12-23
  • On subloops of the loop of invertible elements in the split Cayley–Dickson algebra over a field
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-21
    Evgenii L. Bashkirov

    Abstract This article studies subloops of the Moufang loop of invertible elements in the split Cayley–Dickson algebra over a field K containing a nonassociative subloop formed by elements of the split Cayley–Dickson algebra over a field k such that K is an algebraic extension of k.

    更新日期:2020-12-22
  • On questions related to normal pairs
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-21
    Riyadh Abbas; Ahmed Ayache

    Abstract In this current paper, we identify some new properties concerning normal pairs (R, S). Among other interesting results, we show that every prime ideal P of R that is the radical of a finitely generated ideal A such that AS = S is the radical of an ideal with a basis of two elements. Consequently, we derive a significant improvement of Pendleton’s Criterion by producing further characterizations

    更新日期:2020-12-22
  • Non-Moufang variety of Steiner loops satisfying Moufang’s theorem
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-18
    Marina Rasskazova

    Abstract We construct a non-Moufang variety of Steiner loops H such that every loop from H satisfies Moufang’s theorem. This example solves Rajah’s problem on the existence of such varieties.

    更新日期:2020-12-20
  • Exponents of skew polynomials over periodic rings
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-17
    A. Djamel Bouzidi; Ahmed Cherchem; André Leroy

    Abstract We investigate the properties of periodic rings R in view of studying general skew polynomials f ( t ) ∈ R [ t ; σ , δ ] . We introduce exponents for these polynomials and give some properties of this notion. We show, in particular, that this notion is right-left symmetric. Using the skew evaluation, we generalize the classical connection between the exponent of a polynomial and the order

    更新日期:2020-12-18
  • A criterion for nilpotency of a finite group by the sum of element orders
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-17
    Marius Tărnăuceanu

    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 nilpotent. Moreover, we have ψ ( G ) = 13 21 ψ ( C n ) if and only if n = 6 m with ( 6 , m ) = 1 and G ≅ S 3 × C m . Two interesting consequences of this result are also presented.

    更新日期:2020-12-18
  • Freiman ideals and the number of generators of powers of monomial ideals
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-15
    Ibrahim Al-Ayyoub; Mehrdad Nasernejad

    Abstract Let μ ( I ) denote the number of generators of a monomial ideal I. It is well known that μ ( I k ) < μ ( I k + 1 ) for k ≫ 0 . In this paper we construct monomial ideals I in F [ x , y ] such that μ ( I k + 1 ) < μ ( I k ) for all k ≤ l , given any positive integer l. Also, we extend some results of Eliahou et al. by constructing monomial ideals in R = F [ x 1 , … , x n ] with μ ( I 2 ) <

    更新日期:2020-12-16
  • Irreducibility of integer-valued polynomials I
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-12
    Devendra Prasad

    Abstract Let S ⊂ R be an arbitrary subset of a unique factorization domain R and K be the field of fractions of R. The ring of integer-valued polynomials over S is the set Int ( S , R ) = { f ∈ K [ x ] : f ( a ) ∈ R ∀ a ∈ S } . This article is an effort to study the irreducibility of integer-valued polynomials over arbitrary subsets of a unique factorization domain. We give a method to construct special

    更新日期:2020-12-12
  • The Cayley isomorphism property for the group C 4 × C p 2
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-11
    Grigory Ryabov

    Abstract A finite group G is called a DCI -group if every two isomorphic Cayley digraphs over G are Cayley isomorphic, i.e. their connection sets are conjugate by a group automorphism. We prove that the group C 4 × C p 2 , where p is a prime, is a DCI -group if and only if p ≠ 2 .

    更新日期:2020-12-11
  • Exponential bounds on trace codimensions
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-10
    Allan Berele

    Abstract An algebra with trace function has exponentially bounded codimensions if and only if it satisfies an ordinary polynomial identity and what we call an inter-trace permuting identity, namely one of the form ∑ σ ∈ S n α σ t r ( x 1 y σ ( 1 ) ) ⋯ t r ( x n y σ ( n ) ) = 0 in which not all a σ are zero.

    更新日期:2020-12-10
  • Generalized group determinant gives a necessary and sufficient condition for a subset of a finite group to be a subgroup
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-09
    Naoya Yamaguchi; Yuka Yamaguchi

    Abstract We generalize the concept of the group determinant and prove a necessary and sufficient novel condition for a subset to be a subgroup. This development is based on the group determinant work by Edward Formanek, David Sibley, and Richard Mansfield, where they show that two groups with the same group determinant are isomorphic. The derived condition leads to a generalization of this result.

    更新日期:2020-12-10
  • When is a matrix a sum of involutions or tripotents?
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-09
    Guoli Xia; Gaohua Tang; Yiqiang Zhou

    Abstract We give the necessary and sufficient conditions for an n × n matrix over an integral domain to be a sum of involutions and, respectively, a sum of tripotents. We determine the integral domains over which every n × n matrix is a sum of involutions and, respectively, a sum of tripotents. We further determine the commutative reduced rings over which every n × n matrix is a sum of two tripotents

    更新日期:2020-12-10
  • Additive derivations of incidence algebras
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-09
    Érica Z. Fornaroli; Roger E. M. Pezzott

    Abstract In this paper, we present necessary and sufficient conditions for an additive derivation of an incidence algebra of a connected finite partially ordered set X to be inner. These conditions are related to the structure of X as a directed graph and can be applied for finite partially ordered sets that are not connected or even for some that are not finite.

    更新日期:2020-12-09
  • Existence of primitive pairs with prescribed traces over finite fields
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-09
    Hariom Sharma; R. K. Sharma

    Abstract Let F = F q m ,   m ≥ 7 , n a positive integer, and f = p 1 / p 2 with p 1, p 2 co-prime irreducible polynomials in F [ x ] and deg ( p 1 ) + deg ( p 2 ) = n . We obtain a sufficient condition on (q, m), which guarantees, for any prescribed a, b in E = F q , the existence of primitive pair ( α , f ( α ) ) in F such that Tr F / E ( α ) = a and Tr F / E ( α − 1 ) = b . Further, for every positive

    更新日期:2020-12-09
  • Enlargements of rings
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-08
    Valdis Laan; Kristo Väljako

    Abstract We introduce enlargements of rings as additive analogues of enlargements of semigroups. For example, a full matrix ring over an idempotent ring is an enlargement of that ring. As our main result we prove that two idempotent rings are Morita equivalent if and only if they have a joint enlargement. We also give a necessary and sufficient condition for a ring with left local units to be Morita

    更新日期:2020-12-09
  • Rings additively generated by idempotents and nilpotents
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-07
    Huanyin Chen; Marjan Sheibani Abdolyousefi

    Abstract A ring R is a strongly 2-nil-clean if every element in R is the sum of two idempotents and a nilpotent that commute. A ring R is feebly clean if every element in R is the sum of two orthogonal idempotents and a unit. In this article, strongly 2-nil-clean rings are studied with an emphasis on their relations with feebly clean rings. This work shows new interesting connections between strongly

    更新日期:2020-12-08
  • Classification of ( 2 n − 1 ) -dimensional solvable Leibniz algebras with n-dimensional nilradical
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-07
    Jobir Q. Adashev

    Abstract In this article we study solvable Leibniz algebras with abelian nilradicals. The relation between the dimensions of nilradicals and of the corresponding complemented space to the nilradical is estimated. Moreover, we describe ( 2 n − 1 ) -dimensional solvable Leibniz algebras with n-dimensional nilradical. It is know that the nilradical of these algebras is either n-dimensional abelian algebra

    更新日期:2020-12-08
  • Normal complements for finite groups under coprime action
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-07
    Hangyang Meng

    Abstract Let a finite group A act on a finite group G via automorphism with ( | A | , | G | ) = 1 and let H be a Hall subgroup of G. We prove that if H is a subgroup of C G ( A ) having a normal complement in C G ( A ) , then H has a normal complement in G.

    更新日期:2020-12-07
  • Quadratic (resp. symmetric) Leibniz superalgebras
    Commun. Algebra (IF 0.556) Pub Date : 2020-12-03
    Saïd Benayadi; Fahmi Mhamdi; Salem Omri

    Abstract The aim of this article is to study quadratic Leibniz superalgebras, which are (left or right) Leibniz superalgebras with an even supersymmetric non-degenerate and associative bilinear forms. In particular, we prove that this class of Leibniz superalgebras are symmetric, which are both a left and right Leibniz superalgebras. We give a characterizations of symmetric Leibniz superalgebras. Moreover

    更新日期:2020-12-04
  • On the enhanced power graph of a finite group
    Commun. Algebra (IF 0.556) Pub Date : 2020-11-30
    Ramesh Prasad Panda; Sandeep Dalal; Jitender Kumar

    Abstract The enhanced power graph P e ( 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, independence number, and matching number of enhanced power graphs of finite groups. We first study these graph invariants for P e ( G ) when G is any finite group and then determine them when G

    更新日期:2020-12-01
  • Object-unital groupoid graded rings, crossed products and separability
    Commun. Algebra (IF 0.556) Pub Date : 2020-11-26
    Juan Cala; Patrik Lundström; Hector Pinedo

    Abstract We extend the classical construction by Noether of crossed product algebras, defined by finite Galois field extensions, to cover the case of separable (but not necessarily finite or normal) field extensions. This leads us naturally to consider non-unital groupoid graded rings of a particular type that we call object unital. We determine when such rings are strongly graded, crossed products

    更新日期:2020-11-27
  • The algebraic classification of nilpotent commutative C D -algebras
    Commun. Algebra (IF 0.556) Pub Date : 2020-11-25
    Doston Jumaniyozov; Ivan Kaygorodov; Abror Khudoyberdiyev

    Abstract An algebraic classification of complex 5-dimensional nilpotent commutative C D -algebras is given. This classification is based on an algebraic classification of complex 5-dimensional nilpotent Jordan algebras.

    更新日期:2020-11-25
  • An extension of S-artinian rings and modules to a hereditary torsion theory setting
    Commun. Algebra (IF 0.556) Pub Date : 2020-11-24
    P. Jara

    Abstract For any commutative ring A, we introduce a generalization of S-artinian rings using a hereditary torsion theory σ instead of a multiplicative closed subset S ⊆ A . It is proved that if A is a totally σ-artinian ring, then σ must be of finite type, and A is totally σ-noetherian.

    更新日期:2020-11-25
  • On simple-direct modules
    Commun. Algebra (IF 0.556) Pub Date : 2020-11-23
    Engin Büyükaşık; Özlem Demir; Müge Diril

    Abstract Recently, in a series of papers “simple” versions of direct-injective and direct-projective modules have been investigated. These modules are termed as “simple-direct-injective” and “simple-direct-projective,” respectively. In this paper, we give a complete characterization of the aforementioned modules over the ring of integers and over semilocal rings. The ring is semilocal if and only if

    更新日期:2020-11-25
  • S 2-orbifolds of N = 1 and N = 2 superconformal vertex algebras and W-algebras
    Commun. Algebra (IF 0.556) Pub Date : 2020-11-20
    Hao Li; Antun Milas; Josh Wauchope

    Abstract We study S 2-orbifolds of N = 1 and N = 2 superconformal vertex algebras. For generic values of the central charge, we determine types of these orbifolds and prove that they are W-algebras. For some special rational values of the central charge, we get new examples of rational N = 1 vertex superalgebras. We also investigate S 2-orbifold of the Heisenberg–Virasoro vertex algebra.

    更新日期:2020-11-21
  • Triangular matrix rings of selfinjective rings
    Commun. Algebra (IF 0.556) Pub Date : 2020-11-18
    M. Zahiri; A. Moussavi; R. Mohammadi

    Abstract A module M is said to be generalized extending if for every submodule N ≤ M there exists a direct summand D of M containing N such that D/N is a singular module. In this note we prove that a ring R is right self-injective if and only if the triangular ring T n ( R ) , n ≥ 2 , is right generalized extending. This answers a question which was raised in A. Akalan, G.F. Birkenmeier, A. Tercan

    更新日期:2020-11-18
  • Finite p-groups all of whose proper subgroups of class 2 are metacyclic
    Commun. Algebra (IF 0.556) Pub Date : 2020-11-16
    Pujin Li; Rong Liu

    Abstract In this note, we classify finite p-groups all of whose proper subgroups of nilpotency class equal to 2 are metacyclic.

    更新日期:2020-11-17
  • Fgc extended affine Lie algebras as fixed point subalgebras
    Commun. Algebra (IF 0.556) Pub Date : 2020-11-06
    Hongyan Guo

    Abstract It is known that the centreless cores of fgc extended affine Lie algebras can be viewed as fixed point subalgebras. In this paper, we study fixed point subalgebras of fgc extended affine Lie algebras. Our main result is that the fixed point subalgebras of untwisted extended affine Lie algebras under a finite abelian group (which is determined by some commuting finite order automorphisms) are

    更新日期:2020-11-06
  • Hilbert schemes of two points on K3 surfaces and certain rational cubic fourfolds
    Commun. Algebra (IF 0.556) Pub Date : 2020-11-05
    Genki Ouchi

    Abstract In this article, we check that Fano schemes of lines on certain rational cubic fourfolds are birational to Hilbert schemes of two points on K3 surfaces.

    更新日期:2020-11-05
  • Atomicity and density of Puiseux monoids
    Commun. Algebra (IF 0.556) Pub Date : 2020-11-05
    Maria Bras-Amoros; Marly Gotti

    Abstract A Puiseux monoid is an additive submonoid consisting of non-negative rationals. Although the operation of addition is continuous with respect to the standard topology, the set of irreducibles of a Puiseux monoid is, in general, difficult to describe. Here, we use topological density to understand how much a Puiseux monoid, as well as its set of irreducibles, spread throughout the real line

    更新日期:2020-11-05
  • Birational geometry of defective varieties, II
    Commun. Algebra (IF 0.556) Pub Date : 2020-11-05
    Edoardo Ballico; Claudio Fontanari

    Abstract Let X ⊂ ℙ r be smooth and irreducible and for k ≥ 0 let ν k ( X ) (resp., δ k ( X ) ) be the k-th contact (resp., the k-th secant) defect of X. For all k ≥ 0 we have the inequality ν k ( X ) ≥ δ k ( X ) and in the case k = 1 we characterize projective varieties X for which equality holds, dim Sing ( X ) ≤ δ 1 ( X ) − 1 and the generic tangential contact locus is reducible.

    更新日期:2020-11-05
  • Finite generation of André–Quillen (co-)homology of F-finite algebras
    Commun. Algebra (IF 0.556) Pub Date : 2020-11-04
    Cristodor Ionescu

    Abstract We prove that the André–Quillen homology and cohomology modules of F-finite Z ( p ) -algebras are finitely generated.

    更新日期:2020-11-04
  • On semisimple semirings
    Commun. Algebra (IF 0.556) Pub Date : 2020-10-30
    Jawad Abuhlail; Rangga Ganzar Noegraha

    Abstract We investigate ideal-semisimple and congruence-semisimple semirings. We give several new characterizations of such semirings using e-projective and e-injective semimodules. We extend several characterizations of semisimple rings to (not necessarily subtractive) commutative semirings.

    更新日期:2020-11-02
  • On prime character degree graphs occurring within a family of graphs
    Commun. Algebra (IF 0.556) Pub Date : 2020-10-29
    Jacob Laubacher; Mark Medwid

    Abstract In this article, we investigate families of connected graphs which do not contain an odd cycle in their complement. Specifically, we consider graphs formed by two complete graphs connected in a particular way. We determine which of these graphs can or cannot occur as the prime character degree graph of a solvable group. An obvious expansion and generalization can also be considered, of which

    更新日期:2020-10-30
  • On categorical equivalence of finite p-rings
    Commun. Algebra (IF 0.556) Pub Date : 2020-10-29
    Kalle Kaarli; Tamás Waldhauser

    Abstract We prove that finite categorically equivalent p-rings have isomorphic additive groups (in particular, they have the same cardinality) and that the number of generators is a categorical invariant for finite rings. We also classify rings of size p 3 up to categorical equivalence.

    更新日期:2020-10-30
  • An infinitude of counterexamples to Herzog’s conjecture on involutions in simple groups
    Commun. Algebra (IF 0.556) Pub Date : 2020-10-29
    Chimere Stanley Anabanti; Stefan Hammer; Nneka Chigozie Okoli

    Abstract In 1979, Herzog conjectured that two finite simple groups containing the same number of involutions have the same order. Zarrin, in a 2018 published paper, disproved Herzog’s conjecture with a counterexample. The goal of this article is to prove that there are infinitely many counterexamples to Herzog’s conjecture. In doing so, we obtain an explicit formula for the number of involutions in

    更新日期:2020-10-30
  • On the structure of generalized Jordan *-derivations of prime rings
    Commun. Algebra (IF 0.556) Pub Date : 2020-10-28
    Nadeem Ahmad Dar; Shakir Ali

    Abstract Let R be a noncommutative prime ring with involution ′ * ′ and let Q m s ( R ) be the maximal symmetric ring of quotients of R . In the present paper, we describe the structure of generalized Jordan *-derivations, i.e., additive mappings F : R → R satisfying F ( x 2 ) = F ( x ) x * + x d ( x ) for all x ∈ R , where d is an associated Jordan *-derivation of R . Precisely, we prove that under

    更新日期:2020-10-30
  • Solvable extensions of the naturally graded quasi-filiform leibniz algebra of second type L 5
    Commun. Algebra (IF 0.556) Pub Date : 2020-10-28
    A. Shabanskaya

    Abstract For a sequence of the naturally graded quasi-filiform Leibniz algebra of second type L 5 introduced by Camacho, Gómez, González and Omirov, all the possible right solvable indecomposable extensions over the field C are constructed.

    更新日期:2020-10-30
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