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Axial algebras are a class of commutative non-associative algebras generated by idempotents, called axes, with adjoint action semi-simple and satisfying a prescribed fusion law. Axial algebras were...

We present an explicit minimal set of generators for the defining ideal of the family of Backelin semigroups and find its Betti numbers. In particular, we compute the type of the semigroup as well,...

We classify all decompositions of $M_3(\mathbb{C})$ into a direct vector-space sum of two subalgebras such that one of the subalgebras contains the identity matrix., 29 p

Our first result provides a new characterization of Auslander algebras using a property of hereditary torsion pairs. The second result shows an Auslander algebra $\Lambda$ is left or right glued if and only if $\Lambda$ is representation-finite. Finally, our third result shows the module category of any Auslander algebra contains a tilting module with a particular property, which we call the hereditary property. Applications of this property are investigated.

Let $\Lambda$ be an artin algebra and let $\mathcal{P}^{, Comment: 4 pages

We construct, for any finite commutative ring $R$, a family of representations of the general linear group $\mathrm{GL}_n(R)$ whose intertwining properties mirror those of the principal series for $\mathrm{GL}_n$ over a finite field., 10 pages

D. Prasad showed that the sign of a self-dual representation of a finite or $p$-adic reductive group is often detected by a central element. We study the extension of his results to some more general situations and make some observations about the consequences of his results., To appear in Communications in Algebra

Baer and quasi-Baer rings are important classes of algebraic objects, and their properties have roots in analysis. In this paper, we investigate rings R such that R/ρ(R) is Baer or quasi-Baer, wher...

We find bounds for the number of idempotents in a ring of matrices over an arbitrary finite commutative ring. Using these results, we find a bound on the number of idempotents in an arbitrary finite ring, whereby we improve upon the currently known bounds for the number of idempotents.

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...

In this article, we characterize the super-biderivations of Cartan type Lie superalgebras over the complex field C. Furthermore, we prove that all super-biderivations of Cartan type simple Lie supe...

k-Para-Kahler Lie algebras are a generalization of para-Kahler Lie algebras (k = 1) and constitute a subclass of k-symplectic Lie algebras. In this paper, we show that the characterization of para-...

Let R be a Cohen-Macaulay local ring of dimension d with canonical module ωR. In this article we extend Auslander-Reiten duality theorem to certain R-algebras. As a consequence of our argument, we ...

In this work, we represent free metabelian Leibniz algebras as the wreath product of abelian Leibniz algebras. We obtained an explicit matrix form for the IA-automorphisms of free metabelian Leibni...

In this article, we study C11 r-modules. It is shown that the class of modules with property, each submodule such that the image of its quotient is zero under a left exact preradical has a comple...

We introduce the idea of nei-Noetherian and nei-Artinian modules and rings. We discuss some examples of nei-Noetherian (nei-Artinian) modules and study several properties of them. We characterize t...

In this paper, we derive pre-anti-flexible algebras structures in term of zero weight's Rota-Baxter operators defined on anti-flexible algebras, view pre-anti-flexible algebras as a splitting of anti-flexible algebras, introduce the notion of pre-anti-flexible bialgebras and establish equivalences among matched pair of anti-flexible algebras, matched pair of pre-anti-flexible algebras and pre-anti-flexible bialgebras. Investigation on special class of pre-anti-flexible bialgebras leads to the establishment of the pre-anti-flexible Yang-Baxter equation. Both dual bimodules of pre-anti-flexible algebras and dendriform algebras have the same shape and this induces that both pre-anti-flexible Yang-Baxter equation and $\mathcal{D}$-equation are identical. Symmetric solution of pre-anti-flexible Yang-Baxter equation gives a pre-anti-flexible bialgebra. Finally, we recall and link $\mathcal{O}$-operators of anti-flexible algebras to bimodules of pre-anti-flexible algebras and built symmetric solutions of anti-flexible Yang-Baxter equation., 24 pages

We extend characterizations of inverses along an element to (b, c)-inverses. It is proved that if an element a in a semigroup S is both (b, c)-invertible and (c, b)-invertible for some b,c∈S, then ...

A numerical set is a co-finite subset of the natural numbers that contains zero. Its Frobenius number is the largest number in its complement. Each numerical set has an associated semigroup $A(T)=\{t\mid t+T\subseteq T\}$, which has the same Frobenius number as $T$. For a fixed Frobenius number $f$ there are $2^{f-1}$ numerical sets. It is known that there is a number $\gamma$ close to $0.484$ such that the ratio of these numerical sets that are mapped to $N_f=\{0\}\cup(f,\infty)$ is asymptotically $\gamma$. We identify a collection of families $N(D,f)$ of numerical semigroups such that for a fixed $D$ the ratio of the $2^{f-1}$ numerical sets that are mapped to $N(D,f)$ converges to a positive limit as $f$ goes to infinity. We denote the limit as $\gamma_D$, these constants sum up to $1$ meaning that they asymptotically account for almost all numerical sets., Comment: 13 pages

In this article we prove a version of Glauberman’s Z3*-Theorem for the prime 3 for finite groups G where certain local subgroups are soluble.

Let R be a Gorenstein ring. We first study Gorenstein orthogonal classes and Gorenstein cotorsion pairs of R-modules. Then, we introduce the concept of Gorenstein weak tilting R-modules, which is a...

We study the class of virtually homo-uniserial modules and rings as a nontrivial generalization of homo-uniserial modules and rings. An R-module M is virtually homo-uniserial if, for any finitely g...

The polynomial α=xy∏i=3m(aix+y)∈C[x,y] determines a plane central line arrangement α = 0. We compute explicitly multivariate Bernstein–Sato ideals of α by using the decomposition behavior of the D2...

We study the notion of Cartan-Eilenberg Gorenstein projective N-complexes. We show that an N-complex G is Cartan-Eilenberg Gorenstein projective if and only if Gn, Znt(G),Bnt(G) and Hnt(G) are Gore...

We introduce and study the notion of ES-w-stability for an integral domain R. A nonzero ideal I of R is called ES-w-stable if (I2)w=(JI)w for some t-invertible ideal J of R contained in I, and I is...

Let τn be a type of algebras with the n-ary operation symbols, for a fixed integer n≥1. In this article, we introduce terms of type τn called order-decreasing full terms. We prove that the set of a...

Let D be a principal ideal domain (PID), I be an ideal of D, and X be an indeterminate over D. Let [D;I][X] be the subring of the power series ring D[​[X]​] consisting of all power series f=∑i=0∞ai...

Let Λ be an artin algebra and X be a quasi-resolving subcategory of mod-Λ which is of finite type. Let SX(Λ) be the full subcategory of the morphism category H(Λ) consisting of all monomorphisms f:...

In this work we study some structural properties of the group ηq(G,H), q a non-negative integer, which is an extension of the q-tensor product G⊗qH, where G and H are normal subgroups of some group...

In this paper, we investigate commutativity of rings with involution provided with derivations and generalized derivations satisfying some algebraic identities. Furthermore, we provide examples to ...

A generalized Baumslag–Solitar group (GBS-group) is a finitely generated group acting on a tree with infinite cyclic edge and vertex stabilizers. A group is large if some finite index subgroup maps...

Let F (correspondingly P) denote the abelian category of functors (strict polynomial functors in the sense of Friedlander and Suslin) from finite dimensional vector spaces over Fp to vector spaces ...

In this article, we introduce the product structures and complex structures on hom-Lie superalgebras. First, we give the necessary and sufficient conditions for the existence of product structures ...

Let R be a commutative ring and w be the so-called w-operation on R. Then we introduce and study two concepts of w-FP-injective modules and w-IF rings. To do so, we use two main methods, of which o...

We use bicyclic units to give an explicit construction of a subgroup of UZG isomorphic to the free product of two free abelian groups of rank two, assuming that G is a finite nilpotent group and it...

In this paper, we deal with a particular class of rank two vector bundles (instanton bundles) on the Fano threefold of index one F:=F1×P1. We show that every instanton bundle on F can be described ...

We give a full characterization of the unique Ratliff–Rush complete ideals in the polynomial rings R with two variables over a field. For a class of monomial ideals in R, we investigate the Ratliff...

This note contains two new observations on the linkage properties of quaternion algebras over fields of characteristic 2: first, that a 3-linked field need not be 4-linked (a case which was left open in previous papers) and that three inseparably linked quaternion algebras are also cyclically linked when the base-field is odd-closed.

We give a series of infinite dimensional noncommutative and noncocommutative pointed Hopf algebras, which are Artin-Schelter Gorenstein Hopf algebras with injective dimensions 3. Radford’s Hopf alg...

The exterior degree d∧(G) of a finite group G is the probability that a pair (x, y) of elements x, y chosen uniformly at random in G satisfies x∧y=1∧, where ∧ is the operator of nonabelian exterior...

In this paper, we give a necessary and sufficient condition for a graded algebra to be a McCoy ring. We then classify all McCoy rings of finite dimensional path algebras and truncated algebras over...

In this note I provide two extensions of a particular case of the classical Poncelet theorem.

Characterizations of Morita context rings satisfying various additional ring properties, including reflexive, semiprime, prime, NI, weakly 2-primal and 2-primal, are given. The connections between ...

The purpose of the paper is to introduce and study weakly 2-prime ideals in commutative rings. Let A be a commutative ring with a nonzero identity. A proper ideal P of A is said to be a weakly 2-pr...

Let ω(G) denote the number of orbits on the elements of a group G under the action of its automorphism group. We determine all finite simple groups G such that ω(G)≤100.

An extension of integral domains A⊆B is called a quasi-divisor closed extension if, whenever b1b2∈A for some nonzero b1,b2∈B, then there exist units u, v of B such that b1u,b2v∈A. The notion of a q...

We define a partition of the lattice R-pr of preradicals over pure semisimple hereditary rings, and describe the equivalence classes of the idempotent radicals, which correspond to splitting torsio...

In the present paper, we study the (twisted) 3-canonical map of varieties of Albanese fiber dimension one. Based on a theorem about the regularity of direct image of canonical sheaves, we prove that the 3-canonical map is generically birational when the genus of a general fiber of the Albanese map is 2., Comment: 14 pages

We present an extension, for Banach algebras, of the extension, due to Corach et al, of Jacobson’s lemma on the g-Drazin inverse (Comm. Algebra, 41(2013), 520–531).

We say a lattice L is a subgroup lattice if there exists a group G such that Sub(G)≅L, where Sub(G) is the lattice of subgroups of G, ordered by inclusion. We prove that the lattice of algebraic cl...