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Star operations related to polynomial closure Commun. Algebra (IF 0.7) Pub Date : 2024-03-14 Dario Spirito, Francesca Tartarone
We study polynomial closure of ideals from the point of view of star operations. We show that, if D is an integrally closed domain or a domain of residue characteristic 0, the polynomial closure of...
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Cohomology and homotopy of Lie triple systems Commun. Algebra (IF 0.7) Pub Date : 2024-03-13 Haobo Xia, Yunhe Sheng, Rong Tang
In this paper, first we give the controlling algebra of Lie triple systems. In particular, the cohomology of Lie triple systems can be characterized by the controlling algebra. Then using controlli...
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Composition of generalized derivations acting as a Jordan product in prime rings Commun. Algebra (IF 0.7) Pub Date : 2024-03-12 Balchand Prajapati, Sunil K. Prajapati
Let F, G, and H be generalized derivations with F≠0 on a prime ring R of characteristic different from 2, with Utumi quotient ring U and extended centroid C such that for all r∈RnFH(f(r)2)=F(f(r))G...
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Twisted affine Lie superalgebras and integrability Commun. Algebra (IF 0.7) Pub Date : 2024-03-13 Malihe Yousofzadeh
A twisted affine Lie superalgebra is either a twisted affine Lie algebra or of one of the types X=A(2m−1,2n−1)(2) (m,n≠0, (m,n)≠(1,1) ), A(2m,2n)(4), A(2m,2n−1)(2) or D(m+1,n)(2) (m≥0,n>0 ). It...
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Bialgebras via Manin triples of compatible mock-Lie algebras Commun. Algebra (IF 0.7) Pub Date : 2024-03-12 Karima Benali
Motivated by recent work on compatible mock-Lie algebras such that any linear combination of the two mock-Lie structures is a mock-Lie structure, in this paper we introduce compatible mock-Lie bial...
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On the existence and properties of left invariant k-symplectic structures on Lie groups with bi-invariant peudo-Riemannian metric Commun. Algebra (IF 0.7) Pub Date : 2024-03-12 Ilham Ait Brik, Mohamed Boucetta
k-symplectic manifolds are a convenient framework to study classical field theories and they are a generalization of polarized symplectic manifolds. This paper focus on the existence and the proper...
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Representations and formal deformations of Leibniz H-pseudoalgebras Commun. Algebra (IF 0.7) Pub Date : 2024-03-09 Linlin Liu, Yue Gu
In this paper, we first give some constructions of right (resp. left) Leibniz H-pseudoalgebras and explore the characterization of symmetric Leibniz H-pseudoalgebras. Furthermore, we introduce the ...
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On the number of centralizers and conjugacy class sizes in finite groups Commun. Algebra (IF 0.7) Pub Date : 2024-03-09 Julio C. M. Pezzott
Given a finite group G, denote by cs(G) the set of the sizes of the conjugacy classes of G and by Cent(G) the set of the centralizers of elements of G. Consider a prime p and integers s≥2 and n≥2 ...
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Skew-convex function rings and evaluation of skew rational functions Commun. Algebra (IF 0.7) Pub Date : 2024-03-09 Masood Aryapoor
The product formula for evaluating products of skew polynomials is used to construct a class of rings. As an application, we present a method of evaluating quotients of skew polynomials.
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On simple modules and automorphisms of the quantum Galilei group Commun. Algebra (IF 0.7) Pub Date : 2024-03-07 Tao Lu, Mingfan Xu
This paper is devoted to ring theoretic properties and representations of the quantum Galilei group Fq(G) and its Hopf dual Uq(g) . We classify the primitive ideals and simple modules of Fq(G) an...
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Octonions, Albert vectors and the group E6(F) Commun. Algebra (IF 0.7) Pub Date : 2024-03-06 John N. Bray, Yegor Stepanov, Robert A. Wilson
Abstract–We present a uniform approach to the construction of the groups of type E6 over arbitrary fields without using Lie theory. This gives a simple description of the group generators and some...
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Chern character, infinitesimal Abel-Jacobi map and semi-regularity map Commun. Algebra (IF 0.7) Pub Date : 2024-03-05 Sen Yang
Using Chern character, we construct a natural transformation from the local Hilbert functor to a functor of Artin rings defined from Hochschild homology. This enables us to realize (after slight mo...
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Prime groupoid graded rings with applications to partial skew groupoid rings Commun. Algebra (IF 0.7) Pub Date : 2024-02-29 Paula S. E. Moreira, Johan Öinert
In this paper, we investigate primeness of groupoid graded rings. We provide a set of necessary and sufficient conditions for primeness of a nearly-epsilon strongly groupoid graded ring. Furthermor...
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Ascent and descent of Artinian module structures under flat base changes Commun. Algebra (IF 0.7) Pub Date : 2024-02-28 Tran Do Minh Chau, Le Thanh Nhan
Let φ:R→S be a flat local homomorphism between commutative Noetherian local rings. In this paper, the ascent and descent of Artinian module structures between R and S are investigated. For an Artin...
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Pre-Leibniz algebras Commun. Algebra (IF 0.7) Pub Date : 2024-02-28 Apurba Das
The notion of pre-Leibniz algebras was recently introduced in the study of Rota-Baxter operators on Leibniz algebras. In this paper, we first construct a graded Lie algebra whose Maurer-Cartan elem...
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Logical generation of groups Commun. Algebra (IF 0.7) Pub Date : 2024-02-28 Alireza Abdollahi, Mohammad Shahryari
A group G is called logically generated by a subset S, if every element of G can be defined by a first order formula with parameters from S. We consider the case where G is a direct product of fini...
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Combinatorial Fock spaces and quantum symmetric pairs Commun. Algebra (IF 0.7) Pub Date : 2024-02-22 Michael Ehrig, Kaixuan Gan
A way to construct the natural representation of the quantized affine algebra Uv(sl̂l) is via the deformed Fock space by Misra and Miwa. This relates the classes of Weyl modules for Uq(slN) were q ...
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Chain conditions for rings with enough idempotents with applications to category graded rings Commun. Algebra (IF 0.7) Pub Date : 2024-02-22 Patrik Lundström
We obtain criteria for when a ring with enough idempotents is left/right artinian or noetherian in terms of local criteria defined by the associated complete set of idempotents for the ring. We app...
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On separability of the lattice of τ-closed n-multiply σ-local formations Commun. Algebra (IF 0.7) Pub Date : 2024-02-23 Inna N. Safonova
All groups under consideration are finite. Let σ={σi|i∈I} be some partition of the set of all primes P, G be a group, F be a class of groups, σ(G)={σi|σi∩π(G)≠∅}, and σ(F)=∪G∈Fσ(G).A function f of ...
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Unique maximal Betti diagrams for Artinian Gorenstein k-algebras with the weak Lefschetz property Commun. Algebra (IF 0.7) Pub Date : 2024-02-23 Ben Richert
We give an alternate proof for a theorem of Migliore and Nagel. In particular, we show that if H is an SI-sequence, then the collection of Betti diagrams for all Artinian Gorenstein k-algebras with...
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A criterion for the properness of star-transposition as an involution on n × n matrices over any associative star-ring Commun. Algebra (IF 0.7) Pub Date : 2024-02-23 Michael P. Drazin
On the ring Mn(C) of all n × n complex matrices A, the conjugate transpose involution A↦A* has the “properness” property A*A=0⇒A=0, as required for the existence of the partial order known as the “...
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On pure subrings of sp-groups Commun. Algebra (IF 0.7) Pub Date : 2024-02-22 A. Amini, B. Amini, E. Momtahan
Let G be a sp-group such that for every prime p, Gp is elementary. We show that EndZ(G) is a sp-group and every subring R of ∏EndZ(Gp), containing ⊕EndZ(Gp) is pure if and only if R=MT={x∈∏p∈PEnd(G...
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Idempotent-prime ideals and Baer-type rings with involution Commun. Algebra (IF 0.7) Pub Date : 2024-02-22 Muhammad Saad, Usama A. Aburawsh
In this article, we study some idempotent-structures as cP-Baer rings and I-prime rings. Moreover, we define cP-Baer *-rings and I-*-prime *-rings as involutive versions of cP-Baer rings and I-prim...
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Gorenstein Krull domains and their factor rings Commun. Algebra (IF 0.7) Pub Date : 2024-02-22 Shiqi Xing
The concept of Gorenstein Krull domains can be viewed as a Gorenstein analogue of Krull domains, which are not necessarily integrally closed. This allows us to study those domains from the point vi...
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Strong Gelfand pairs of SL(2,pn) Commun. Algebra (IF 0.7) Pub Date : 2024-02-22 Jordan C. Gardiner, Stephen P. Humphries
A strong Gelfand pair (G, H) is a group G together with a subgroup H such that every irreducible character of H induces a multiplicity-free character of G. We classify the strong Gelfand pairs of t...
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Integer-valued polynomials on subsets of upper triangular matrix rings Commun. Algebra (IF 0.7) Pub Date : 2024-02-19 A. R. Naghipour, J. Sedighi Hafshejani
S. Frisch, showed that the integer-valued polynomials on upper triangular matrix ring IntTn(K)(Tn(D)):={f∈Tn(K)[x]|f(Tn(D))⊆Tn(D)} is a ring, where D is an integral domain with field of fractions K...
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On Hopf algebras whose coradical is a cocentral abelian cleft extension Commun. Algebra (IF 0.7) Pub Date : 2024-02-21 G. A. García, M. Mastnak
This paper is a first step toward the full description of a family of Hopf algebras whose coradical is isomorphic to a semisimple Hopf algebra Kn , n an odd positive integer, obtained by a cocentra...
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Footnotes to a footnote of a paper by Fano Commun. Algebra (IF 0.7) Pub Date : 2024-02-20 Ciro Ciliberto
Following a suggestion in a footnote of the paper [1] by Fano, we give a direct proof of the fact that one of the two Fano threefolds of degree 72 in P38 is isomorphic to the anticanonically embedd...
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Coherence and weak factoriality in a certain pullback Commun. Algebra (IF 0.7) Pub Date : 2024-02-19 Xiaolei Zhang, Gyu Whan Chang, Hwankoo Kim, Dechuan Zhou
Let D be a domain with its quotient field K. Let K[θ]=K[x]/(xn) where x is an indeterminate and θ=x+(xn). Denote by Rn=D+θK[θ], which is a subring of K[θ]. This paper studies several properties of ...
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On NN-torsion-free and NN-injective modules Commun. Algebra (IF 0.7) Pub Date : 2024-02-19 Wei Zhao, Yungui Liu, Zhigao Dong, Yuxin Wei
In this paper, we introduce the concept of NN-torsion-free modules (respectively, NN-injective modules) as a generalization of nonnil-torsion-free modules (respectively, injective modules). We show...
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Drinfeld twists of Koszul algebras Commun. Algebra (IF 0.7) Pub Date : 2024-02-22 Edward Jones-Healey
Given a Hopf algebra H and a counital 2-cocycle μ on H, Drinfeld introduced a notion of twist which deforms an H-module algebra A into a new algebra Aμ. We show that when A is a quadratic algebra, ...
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Generalized sharped cubic form and split spin factor algebra Commun. Algebra (IF 0.7) Pub Date : 2024-02-22 Vsevolod Gubarev, Farukh Mashurov, Alexander Panasenko
There is a well-known construction of a Jordan algebra via a sharped cubic form. We introduce a generalized sharped cubic form and prove that the split spin factor algebra is induced by this constr...
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Bridgeland stability conditions and skew lines on ℙ3 Commun. Algebra (IF 0.7) Pub Date : 2024-02-19 Sammy Alaoui Soulimani, Martin G. Gulbrandsen
Inspired by Schmidt’s work on twisted cubics, we study wall crossings in Bridgeland stability, starting with the Hilbert scheme Hilb2m+2(P3) parametrizing pairs of skew lines and plane conics union...
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Lie algebras associated with labeled directed graphs Commun. Algebra (IF 0.7) Pub Date : 2024-02-19 Mauricio Godoy Molina, Diego Lagos
We construct 2-step nilpotent Lie algebras using labeled directed simple graphs and give a criterion to detect certain ideals and subalgebras by finding special subgraphs. We prove that if a label ...
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On the isomorphism problem for certain p-groups Commun. Algebra (IF 0.7) Pub Date : 2024-02-17 Alexander Montoya Ocampo, Fernando Szechtman
We consider 9 infinite families of finite p-groups, for p a prime, and we settle the isomorphism problem that arises when the parameters that define these groups are modified.
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n-absorbing ideal factorization in commutative rings Commun. Algebra (IF 0.7) Pub Date : 2024-02-13 Hyun Seung Choi
In this article, we show that Mori domains, pseudo-valuation domains, and n-absorbing ideals, the three seemingly unrelated notions in commutative ring theory, are interconnected. In particular, we...
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A note on the image of polynomials on upper triangular matrix algebras Commun. Algebra (IF 0.7) Pub Date : 2024-02-14 Qian Chen
In the present paper we shall obtain the following result: Let n≥2 and m≥1 be integers. Let p(x1,…,xm) be a polynomial with zero constant term in non-commutative variables over an algebraically clo...
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Laurent polynomial identities on symmetric units of group algebras Commun. Algebra (IF 0.7) Pub Date : 2024-02-14 M. Akbari-Sehat, M. Ramezan-Nassab
Let F be an infinite field of characteristic p≠2, G be a group, and * be an involution of G extended linearly to an involution of the group algebra FG. In the literature, group identities on units ...
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Local method for compositional inverses of permutation polynomials Commun. Algebra (IF 0.7) Pub Date : 2024-02-14 Pingzhi Yuan
In this paper, we provide a local method to find compositional inverses of all PPs, some new PPs and their compositional inverses are given.
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Straight domains are locally divided Commun. Algebra (IF 0.7) Pub Date : 2024-02-14 Spencer Secord
We present a proof that all straight domains are locally divided—thereby answering two open problems posed by Dobbs and Picavet, which appeared in the survey “Open Problems in Commutative Ring Theo...
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Profinite version of the Beckmann-Black problem Commun. Algebra (IF 0.7) Pub Date : 2024-02-14 Nour Ghazi
The Beckmann-Black problem asks whether any given finite Galois extension E/K of group G is the specialization at some point t0∈P1(K) of some finite regular Galois extension F/K(T) with the same gr...
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Subvarieties of hypersurface sections of generalized Grassmannians Commun. Algebra (IF 0.7) Pub Date : 2024-02-09 Takeshi Abe
Consider a generalized Grassmannian G/P⊂P embedded in a projective space by a complete linear system of a positive generator of the Picard group. For a very general hypersurface H⊂P , we study sub...
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On the Galois group of a reciprocal even octic polynomial Commun. Algebra (IF 0.7) Pub Date : 2024-02-09 Chad Awtrey, Frank Patane
Let F be a field of characteristic 0, and let f(x)=x8+ax6+bx4+ax2+1∈F[x] be irreducible with Galois group Gal(f) . We extend results in the literature to give a complete and elementary classificat...
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The center of infinitesimal q-Schur algebra sq(2,r)1 Commun. Algebra (IF 0.7) Pub Date : 2024-02-09 Wenting Gao, Shiyuan Liu
In this paper, we obtain a basis for the center of the infinitesimal q-Schur algebra sq(2,r)1 in terms of its certain basis.
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On wonderful compactifications of SL(2,𝔽) for non-Archimedean local fields 𝔽 Commun. Algebra (IF 0.7) Pub Date : 2024-02-09 Corina Ciobotaru
We compute the wonderful compactification of symmetric varieties of SL(2,F) , where F is a finite field-extension of Qp with p≠2 , that comes from either an abstract or an F -involution of SL(2,F...
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Remarks on almost Gorenstein rings Commun. Algebra (IF 0.7) Pub Date : 2024-02-07 Naoki Endo, Naoyuki Matsuoka
This paper investigates the relation between the almost Gorenstein properties for graded rings and for local rings. Once R is an almost Gorenstein graded ring, the localization RM of R at the grade...
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Relative injective envelopes and relative projective covers on ring extensions Commun. Algebra (IF 0.7) Pub Date : 2024-02-06 Shufeng Guo
A ring extension is a ring homomorphism preserving identities. In this paper, we give the definitions of relative injective envelopes and relative projective covers of modules on ring extensions, a...
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Complemented zero-divisor graphs associated with finite commutative semigroups Commun. Algebra (IF 0.7) Pub Date : 2024-02-06 Chase Bender, Paul Cappaert, Rachelle DeCoste, Lisa DeMeyer
Let S be a commutative semigroup with zero. The zero-divisor graph associated with S is the simple graph whose vertex set is given by the nonzero zero-divisors of S where two distinct vertices are ...
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An injective-envelope-based characterization of distributive modules over commutative Noetherian rings Commun. Algebra (IF 0.7) Pub Date : 2024-02-06 E. Enochs, M. R. Pournaki, S. Yassemi
Let R be a commutative Noetherian ring and M be an R-module. The R-module M is called distributive if for every submodules S, T and U of M, the equality S∩(T+U)=S∩T+S∩U holds true. In this paper, w...
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Collections of an ideal: any n-absorbing ideal is strongly n-absorbing Commun. Algebra (IF 0.7) Pub Date : 2024-02-05 Spencer Secord
We show that any n-absorbing ideal must be strongly n-absorbing, which is the first of Anderson and Badawi’s three interconnected conjectures on absorbing ideals. We prove this by introducing and s...
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On the structure of finite groups determined by the arithmetic and geometric means of element orders Commun. Algebra (IF 0.7) Pub Date : 2024-01-31 Valentina Grazian, Carmine Monetta, Marialaura Noce
In this paper we consider two functions related to the arithmetic and geometric means of element orders of a finite group, showing that certain lower bounds on such functions strongly affect the gr...
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Contact and Frobenius Lie superalgebras Commun. Algebra (IF 0.7) Pub Date : 2024-02-01 M. C. Rodríguez-Vallarte, G. Salgado
We introduce the concepts of complex finite-dimensional contact and Frobenius Lie superalgebras, including some relevant examples of this type of Lie superalgebras. We establish some basic properti...
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The characterization of PSL(2, p) (p≡±5 (mod 24)) Commun. Algebra (IF 0.7) Pub Date : 2024-01-30 Yunfei Guan, Quanfu Yan, Zhencai Shen
Let G be a finite group. A vanishing element of G is an element g∈G such that χ(g)=0 for some irreducible complex character χ of G. We will denote by Van(G) the set of vanishing elements of G and b...
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A Schur ring approach to supercharacters of groups associated with finite radical rings Commun. Algebra (IF 0.7) Pub Date : 2024-01-30 Carlos A. M. André, Pedro J. Freitas, Tânia Z. Silva
We consider the central Schur ring associated with the standard supercharacters of the adjoint group G(A) of a finite radical ring A , and define supercharacters of the subgroup CG(A)(σ) consisti...
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Factorization properties of quotients of polynomial and power series rings by monomial ideals Commun. Algebra (IF 0.7) Pub Date : 2024-01-27 Ashkan Nikseresht, Shahin Rahimi
Suppose that K is a field, S=K[x1,…,xn] or S=K[[x1,…,xn]] and I is a monomial ideal of S. We study factorization properties of the ring R=S/I . In particular, we present conditions equivalent to ...
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Dual modules, f-projective modules and Π-coherence over trivial ring extensions Commun. Algebra (IF 0.7) Pub Date : 2024-01-27 Lixin Mao
Let R⋉M be a trivial extension of a ring R by an R-R-bimodule M. We first describe explicitly the structure of a dual module over R⋉M . Then we characterize Mittag-Leffler modules and f-projective...
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The (ET4) axiom for extriangulated categories Commun. Algebra (IF 0.7) Pub Date : 2024-01-27 Xiaoxue Kong, Zengqiang Lin, Minxiong Wang
Extriangulated categories were introduced by Nakaoka and Palu, which is a simultaneous generalization of exact categories and triangulated categories. Axiom (ET4) for extriangulated categories is a...
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On completely decomposable defining equations of finite sets in Pn Commun. Algebra (IF 0.7) Pub Date : 2024-01-22 Jaeheun Jung, Euisung Park
Let I(Γ) be the homogeneous ideal of a finite set Γ in Pn of d points in linearly general position. In 1972, Saint-Donat proved that if d≤2n then I(Γ) is generated by completely decomposable quadra...
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A remark on the moduli space of Lie algebroid λ-connections Commun. Algebra (IF 0.7) Pub Date : 2024-01-22 Parul Keshari, Anoop Singh
Let X be a compact Riemann surface of genus g≥3. Let L=(L,[.,.],♯) be a holomorphic Lie algebroid over X of rank one and degree (L)<2−2g. We consider the moduli space of holomorphic Lλ-connections ...
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Fano 4-folds with nef tangent bundle in positive characteristic Commun. Algebra (IF 0.7) Pub Date : 2024-01-27 Yuta Takahashi, Kiwamu Watanabe
In characteristic 0, the Campana-Peternell conjecture claims that the only smooth Fano variety with nef tangent bundle should be homogeneous. In this paper, we study the positive characteristic ver...