Journal of Algebra and Its Applications

A subgroup [Formula: see text] of a group [Formula: see text] is called a TI-subgroup of [Formula: see text] if [Formula: see text] or [Formula: see text] for each [Formula: see text] [Formula: see text][Formula: see text]. Furthermore, let [Formula: see text] be a partition of the set of all primes [Formula: see text], a subgroup [Formula: see text] of [Formula: see text] is called [Formula: see…

Let [Formula: see text] be a [Formula: see text]-torsion free unital *-ring, possessing a non-trivial symmetric idempotent. In the present paper, we discuss that, under certain mild conditions on [Formula: see text], a map [Formula: see text] : [Formula: see text] (not necessarily additive) satisfies [Formula: see text] for all [Formula: see text] if and only if it is an additive *-derivation. Fu…

Let [Formula: see text] be a Morita ring such that the bimodule homomorphisms are zero. In this paper, we give sufficient conditions for a [Formula: see text]-module [Formula: see text] to be strongly Ding projective. Moreover, we describe all strongly Ding projective modules over the [Formula: see text] matrix algebra [Formula: see text] over [Formula: see text].

We classify reflectable bases of an affine root system of type [Formula: see text] in terms of a directed graph with weighted edges corresponding to a reflectable base.

Let [Formula: see text] be an algebra over a field K, and let mod[Formula: see text] denote the category of right [Formula: see text]modules. This paper introduces the conception of a uniform McCoy module pair. We show that if two objects of [Formula: see text] is a uniform McCoy module pair, then their direct sum is a McCoy module. Furthermore, let [Formula: see text] be a quiver of type [Formul…

In combinatorial commutative algebra, to characterize the Cohen-Macaulayness of some classes of graphs is an important topic. In this paper, we give complete characterizations for the Cohen-Macaulayness of two classes of clutters. One is interval clutters, a subclass of 𝛽-acyclic clutters; the other is 𝛽-cycles.

Let [Formula: see text] be a finite chain with [Formula: see text] elements and [Formula: see text] be the semigroup of all injective order-preserving partial transformations of [Formula: see text]. For any nonempty subset [Formula: see text] of [Formula: see text], let [Formula: see text] be the subsemigroup of [Formula: see text] of all transformations with range contained in [Formula: see text…

We investigate structural decompositions in rings that reflect partial forms of unit-regularity, focusing on containment conditions between principal and idempotent-generated ideals. Motivated by canonical decompositions such as R = Ra ⨁ R(a − u) arising in unit-regular rings, we explore configurations where such decompositions persist under weaker assumptions. Using outer inverse techniques, we …

We generalize a well-known result proved by Filaseta and Trifonov in 2002 that the Bessel polynomials of all degrees are irreducible over the field of rational numbers. The proof given here of our generalization appears to be simpler than the known proofs of Filaseta-Trifonov Theorem. We use some recent results by Lehmer, Luca, Najman and Shorey regarding the largest prime divisor of a product of…

We generalize a result of Araki (1985) on indecomposable group representations with invariant (necessarily indefinite) inner product and irreducible subrepresentation to Hopf *-algebras. Moreover, we characterize invariant inner products on the projective indecomposable representations of small quantum groups U qsl(2) at odd roots of unity and on the indecomposable representations of generalized …

Let R be a commutative ring with identity. In this paper, we introduce and investigate the second ideal intersection graph SII(R) of R whose vertices are the non-zero proper ideals of R and two distinct vertices I and J are adjacent if and only if I ∩ J is a second ideal of R.

In this paper, we study superbiderivations on Lie superalgebras from structural and geometric perspectives. Motivated by the classical fact that the bracket of a Lie algebra is itself a biderivation, we propose a new definition of superbiderivation for Lie superalgebras—one that requires the bracket to be a superbiderivation, a condition not satisfied by existing definitions in the literature. Ou…

We study simple graphs for which the maximal homogeneous ideal is an associated prime of the second power of their closed neighborhood ideals. In particular, we show that such graphs must have diameter at most 6, that this bound is sharp, and that those with diameter 2 are precisely the vertex diameter-2-critical graphs.

In this paper, we systematically investigate the characterization of SEP elements in an involution ring, using the solvability of an equation in a specific set as a necessary and sufficient criterion. Building on this, we establish a series of characterizations by analyzing the relationships between SEP elements and the followings: the projectivity of generalized inverse products, the projectivit…

In this paper, we present a new free field(-like) construction of irreducible modules for toroidal 𝔰𝔩 2 with finite dimensional weight spaces and trivial central action. To this end, we also determine the irreducibility of certain Verma modules for generalized Takiff algebras associated to 𝔰𝔩 2 .

In this paper, we extend the concept of para-Kähler structures from Lie algebras to left Leibniz algebras. First, we show that the Levi-Civita product, initially defined for pseudo-Euclidean Lie algebras, can be generalized to any pseudo-Euclidean algebra. A para-Kähler left Leibniz algebra is defined as a para-Kähler vector space [Formula: see text] equipped with a left Leibniz product [Formula:…

Let [Formula: see text] be a finite group. For a complex irreducible character [Formula: see text] of [Formula: see text], the number [Formula: see text] is called the codegree of [Formula: see text]. Our aim here is to study the relationship between the structure of [Formula: see text] and the codegrees of real-valued strongly monolithic characters of [Formula: see text]. We obtain new bounds on…

The algebraic and geometric classifications of complex 3-dimensional transposed [Formula: see text]-Poisson algebras are given. Namely, we prove that the variety of complex 3-dimensional transposed [Formula: see text]-Poisson algebras has dimension 9 and 7 irreducible components for [Formula: see text] the variety of complex 3-dimensional transposed (-1)-Poisson algebras has dimension 9 and 5 irr…

Here we describe the least distributive lattice congruence [Formula: see text] on an idempotent semiring in general and characterize the varieties [Formula: see text], [Formula: see text] and [Formula: see text] of all idempotent semirings such that [Formula: see text], [Formula: see text] and [Formula: see text], respectively. If [Formula: see text], then the multiplicative reduct [Formula: see …

The Grassmannian 𝒢 2,m , is the collection of all 2 dimensional subspaces of a vector space of dimension m. It is one of the most widely studied objects in Algebraic Geometry and has interesting algebraic, geometric, and combinatorial properties. Since subspaces of dimension 2 are known as lines the Grassmannian 𝒢 2,m , is known as the Grassmannian of lines. A class of linear codes, known as Gr…