Abstract 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 called weakly ES-w-stable if Iw=(JE)w for some t-invertible fractional ideal J of R and w-idempotent fractional ideal E of R. We define R to be an ES-w-stable domain (resp., a weakly ES-w-stable

Abstract A finite group G is called a PST-group (respectively, PT-group, T-group) if every subnormal subgroup of G is Sylow permutable (respectively, permutable, normal) in G. Let F be a class of group and G a finite group. Then, a set Σ of subgroups of G is called a G-covering subgroup system for the class F if G∈F whenever Σ⊆F. We prove that: (i) If a set of subgroups Σ of G contains at least one

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, we determine all rational functions of degree four that permute P1(Fq).

Abstract Let G be a finite group. For a character χ of G, the number cod(χ)=[G:kerχ]χ(1) is called the co-degree of χ. Let N be a non-trivial normal subgroup of G and set Irr(G|N)=Irr(G)−Irr(G/N). In this paper, we show that if for every χ,ψ∈Irr(G|N) with cod(χ)≠cod(ψ), the greatest common divisor of cod(χ) and cod(ψ) is either 1 or a prime, then N is solvable.

Abstract Necessary and sufficient conditions for a Markov chain to be ergodic are that the chain is irreducible and aperiodic. This result is manifest in the case of random walks on finite groups by a statement about the support of the driving probability: a random walk on a finite group is ergodic if and only if the support is not concentrated on a proper subgroup, nor on a coset of a proper normal

Abstract An element a in a ring R is left uniquely generated (or left UG) if, whenever Ra = Rb, a = ub for a unit u in R, and is left strongly UG if, whenever Ra = Rb, a = ub = bu for a unit u in R. A ring is a left UG (resp. left strongly UG) ring if each of its elements is left UG (resp. left strongly UG). Motivated by a result of Marks [15 Marks, G.A. (2006). A criterion for unit-regularity. Acta

Abstract 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 all order-decreasing full terms of type τn is closed under the superposition operation; and hence it forms an algebra denoted by MAODn(τn). Moreover, we prove that MAODn(τn) is a Menger algebra of

Abstract Let R and S be commutative rings with identity, f:R→S a ring homomorphism and J an ideal of S. Then, the subring R⋈fJ:={(a,f(a)+j)|a∈R and j∈J} of R × S is called the amalgamation of R with S along J with respect to f. In this article, we investigate when two extended ideals in R⋈fJ of R are linked.

Abstract Let R be a commutative ring with nonzero identity. Yassine et al. defined the concept of 1-absorbing prime ideals as follows: a proper ideal I of R is said to be a 1-absorbing prime ideal if whenever xyz∈I for some nonunit elements x,y,z∈R, then either xy∈I or z∈I. We use the concept of 1-absorbing prime ideals to study those commutative rings in which every proper ideal is a product of 1-absorbing

Abstract 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:A→B in X such that Cokerf also lies in X. In this paper, we state and prove Brauer-Thrall type theorems for SX(Λ). As applications, we provide necessary and sufficient conditions for the submodule

Abstract 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∞aiXi in D[​[X]​] such that ai∈I for all large i. By definition, the polynomial ring D[X] and the power series ring D[​[X]​] are special cases of [D;I][X] when I=(0) and I = D, respectively. In this

Abstract A classical problem in nonassociative algebras involves the existence of simple finite-dimensional commutative nilalgebras. In this paper, we study the class Ω of nonassociative algebras satisfying the identity (xy)2=x2y2 over a field of characteristic different from 2 and 3. We show that every unitary algebra in Ω is associative. Next, we prove that each prime algebra in Ω is either associative

Abstract 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 show that various restrictions in the hypotheses of our theorems are not superfluous.

Abstract 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 L. We establish by simple arguments some closure properties of ηq(G,H) when G and H belong to certain Schur classes. This extends similar results concerning the case q = 0 found in the literature

Abstract 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 onto the free group F2. An explicit description is given for all index n subgroups in non-large GBS groups. Moreover, we give exact formulas for the numbers of subgroups, normal subgroups, and conjugacy

Abstract 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 over Fp. These two categories are related via the exact forgetful functor ι:P→F. The category F is strongly related to topology and representation theory of symmetric and general linear groups but

Abstract 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 and complex structures, respectively. Then, we study special product structures and complex structures, respectively, and accordingly give different decompositions of hom-Lie superalgebras. Finally

Abstract In this article, we generalize some special ideals to crossed modules and give some relations. Also, we prove one of the existence results in algebra for crossed modules using Zorn’s lemma that a crossed module with nontrivial base ring with unity contains a maximal crossed ideal.

Abstract The Abel-Jacobi maps generalize the usual Jacobi map for curves to the case of nonsingular complex projective varieties. Here, we study certain Abel-Jacobi maps on the moduli space of parabolic stable bundles of fixed rank, determinant and generic weight over a nonsingular complex projective curve. We prove that the maps are split surjections.

Abstract 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 one is to localize at maximal w-ideals of R and the other is to utilize w-Nagata modules over w-Nagata rings. As an application, we characterize Prüfer v-multiplication domains in terms of w-FP-injective

Abstract We describe all the twisted tensor products of K3 with K3, where K is an arbitrary field.

Abstract 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 as the cohomology of a monad whose terms are free sheaves. Furthermore we prove the existence of instanton bundles for any admissible second Chern class and we construct a nice component of the moduli

Abstract We propose the notion of GAS numerical semigroup which generalizes both almost symmetric and 2-AGL numerical semigroups. Moreover, we introduce the concept of almost canonical ideal which generalizes the notion of canonical ideal in the same way almost symmetric numerical semigroups generalize symmetric ones. We prove that a numerical semigroup with maximal ideal M and multiplicity e is GAS

Abstract This letter is divided in two parts. In the first one it will be shown that the datum of a post-Lie product is equivalent to the one of an invertible crossed morphism between two Lie algebras. Moreover it will be argued that the integration of such a crossed morphism yields the post-Lie Magnus expansion associated to the original post-Lie algebra. The second part is devoted to present two

Abstract 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 contains an element g of odd prime order such that the subgroup 〈g〉 is not normal in G. To do this we first construct a subgroup isomorphic to the desired free product inside GL(2,C) and then we

Abstract 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–Rush behavior of powers of these ideals and also the depth of their associated graded ring. Namely, we give some sufficient and some necessary conditions for this depth to be positive. The results

Abstract We explicitly describe the divisor class groups and semidualizing modules for ladder determinantal rings with coefficients in an arbitrary normal domain for arbitrary ladders, not necessarily connected, and all sizes of minors.

Abstract 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.

Abstract We characterize all (n−2)-dimensional linear subspaces of Pn such that the induced linear projection, when restricted to the rational normal curve, gives a Galois morphism. We give an explicit description of these spaces as a disjoint union of locally closed subvarieties in the Grassmannian G(n−2,n).

Abstract We study ideals in a local ring R whose quotient rings induce large homomorphisms of local rings. We characterize such ideals in terms of the maps of Koszul homologies over several classes of local rings, including complete intersections, Koszul rings, and some classes of Golod rings.

Abstract Let n and t be non-negative integers, R a commutative Noetherian ring with dim(R)≤n+2,a an ideal of R, M and N finite R-modules, and X an arbitrary R-module. We prove that if ExtRi(M/aM,X) is an FD

Abstract In this paper, we investigate Lie generalized derivations on bound quiver algebras associated with a finite acyclic quiver. The first main result shows that every bound quiver algebra associated with a finite acyclic quiver has the properness Lie generalized derivation property. The second main result investigates the uniqueness property. Namely, among other things, we show that a bound quiver

Abstract Let G be a finite group and cd(G) denote the set of complex irreducible character degrees of G. We prove that if H≇2.M12 is a sporadic quasisimple group that cd(G)=cd(H), then there exists an Abelian subgroup A of G such that G is isomorphic to a central product of H and A.

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

Abstract The aim of this article is to provide an answer to the C[∂]-split extending structures problem for Leibniz conformal algebras, which asks that how to describe all Leibniz conformal algebra structures on E=R⊕Q up to an isomorphism such that R is a Leibniz conformal subalgebra. For this purpose, a unified product of Leibniz conformal algebras is introduced. Using this tool, two cohomological

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.

Abstract For an element w of a simply-laced Weyl group, Buan-Iyama-Reiten-Scott defined a subcategory F(w) of the module category over the preprojective algebra of Dynkin type. This paper studies categorical properties of F(w) using the root system. We show that simple objects in F(w) bijectively correspond to Bruhat inversion roots of w, and obtain a combinatorial criterion for F(w) to satisfy the

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

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

Abstract We determine some Nichols algebras that admit a nontrivial quadratic relation associated to some families of upper triangular solutions of the Yang–Baxter equation of dimension 3.

Abstract Let G be a finite group and σ1(G)=1|G|∑H≤G|H|. Answering to a problem posed by M. Tărnăuceanu, we prove that, if σ1(G)<11720, then G is solvable.

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 [lr]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 domain

Abstract Given elements a, b, c of any associative ring R with 1, then a is called right hybrid (b, c)-invertible if there exists y∈R such that yay=y,yR=bR and rann (y)=rann(c). It is shown that such y exists if and only if c∈cabR and rann(cab)⊆rann(b), in which case y is unique. With an appropriate generalization of the right annhilator rann (.), this result is extended to all semigroups with 1 and

Abstract 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 algebra and Gelaki’s Hopf algebra are homomorphic images of these Hopf algebras. We determine the irreducible representations of them. We describe the Grothendieck rings of them. We obtain that two

Abstract 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 square G∧G and 1∧ neutral element in G∧G. The probability d(G) that two elements of G commute is related to d∧(G). Of course, d(G) = 1 iff G is abelian, but d∧(G)=1 iff G is cyclic, so we detect

Abstract 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 field K. This leads a new way of constructing McCoy rings.

Abstract In this note we provide two extensions of a particular case of Poncelet theorem.

Abstract 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 characterizations of reflexive, semiprime and prime Morita context rings are outlined and shown to be related to torsionless and faithful modules. Similarly, the characterizations of NI, weakly

Abstract Let R⊆E be two Lie conformal algebras and Q be a given complement of R in E. Classifying complements problem asks for describing and classifying all complements of R in E up to an isomorphism. It is known that E is isomorphic to a bicrossed product of R and Q. We show that any complement of R in E is isomorphic to a deformation of Q associated to the bicrossed product. A classifying object

Abstract A semigroup is called a Hua semigroup if any mapping h:S→S satisfying (∀a,b∈S) h(ab)=h(a)h(b) or h(b)h(a) is either a homomorphism or an anti-homomorphism. We use this name for such a semigroup since it is relevant to a well-known result in ring theory, which is established by L. K. Hua in 1949. C. M. Reis and H. J. Shyr first translated Hua’s result from rings to semigroups in 1977. In this

Abstract 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.

Abstract There are five non-isomorphic groups of order 18. Of these two groups are abelian and the rest are non-abelian. In this article, we give the structures of the unit groups of the finite group algebras of all groups of order 18, i.e., U(FC18),U(FD18),U(F(D6×C3)),U(F(C32⋊C2)) and U(F(C6×C3)), where F is a finite field.

Abstract In this note, we give necessary and sufficient conditions for which the absorption laws and the reverse order laws of two kinds of generalized core inverses hold.

Abstract In this paper we provide necessary and sufficient conditions for a formal power series g over R or C to have formal power series g1/k such that (g1/k)k=g for all positive integers k or for some positive integers. The algorithms of computing such formal root series are also provided. Moreover, we investigate the uniqueness of formal root series if there exists.

Abstract We investigate conditions on an R-module M that are analogous to Gabriel’s condition H for the ring R.

Abstract 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-prime ideal if whenever 0≠xy∈P for some x,y∈A, then x2∈P or y2∈P. Besides giving various examples and characterizations of weakly 2-prime ideals, we investigate the relations between weakly 2-prime

Abstract Suppose Γ is a finite simple graph. If D is a dominating set of Γ such that each x∈D is contained in the set of vertices of an odd cycle of Γ, then we say that D is an odd dominating set for Γ. For a finite group G, let Δ(G) denote the character graph built on the set of degrees of the irreducible complex characters of G. In this paper, we show that the complement of Δ(G) contains an odd dominating

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 notion of δ-primary hyperideals in Krasner (m, n)-hyperrings, which unifies the prime and primary hyperideals under one frame. Moreover, we introduce and investigate the notions of 2-absorbing δ-primary

Abstract 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 quasi-divisor closed extension is a generalization of that of a divisor closed extension. In this article, we prove some new results about divisor closed extensions and quasi-divisor closed extensions

Abstract 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.