环与代数

We studied linear mappings in Beidleman near-vector spaces and explored their matrix representations using $R$-bases of $R$-subgroups. Additionally, we developed algorithms for determining the seed number and seed sets of $R$-subgroups…

In this paper, we first construct a differential graded Lie algebra that controls deformations of a Lie-Yamaguti algebra. Furthermore, a relative Rota-Baxter operator on a Lie-Yamaguti algebra is characterized as a Maurer-Cartan element in…

A classical theorem by Jacobson says that a ring in which every element $x$ satisfies the equation $x^n=x$ for some $n>1$ is commutative. According to Birkhoff's Completeness Theorem, if $n$ is fixed, there must be an equational proof of…

Given a two-sided noetherian ring $A$ with a dualizing complex, we show that the big finitistic dimension of $A$ is finite if and only if every bounded below Gorenstein-projective-acyclic cochain complex of Gorenstein-projective $A$-modules…

Let $K$ be an algebraically closed field of characteristic zero, $P_n=K[x_1, ..., x_n]$ the polynomial ring, and $W_n(K)$ the Lie algebra of all $K$-derivations on $P_n$. One of the most important subalgebras of $W_n(K)$ is the triangular…

In this paper we consider endomorphisms of an undirected cycle graph from Semigroup Theory perspective. Our main aim is to present a process to determine sets of generators with minimal cardinality for the monoids $wEnd(C_n)$ and $End(C_n)$…

We find necessary and sufficient conditions for the finite separability of finitely generated commutative rings. Namely, we prove that every such ring is a finite extension of its torsion ideal $I_k$ where $k$ is square-free, and $I_k$ is a…

Let $L/K$ be a cyclic extension of degree $n = 2m$. It is known that the space $\text{Alt}_K(L)$ of alternating $K$-bilinear forms (skew-forms) on $L$ decomposes into a direct sum of $K$-subspaces $A^{\sigma^i}$ indexed by the elements of…

Each $\frac{1}{2}$-derivation of the planar Galilean conformal algebra is proven to be a scalar. As a corollary, all transposed Poisson structures on the planar Galilean conformal algebra are trivial.

We provide a simple natural duality for the varieties generated by the negation- and implication- free reduct of a finite MV-chain. We study these varieties through the dual equivalence thus obtained. For example, we fully characterize…

In this paper, we first introduce stable functors with respect to a preenveloping/precovering subcategory and investigate some of their properties. Using that we then introduce and study a relative complete cohomology theory in abelian…

We say that a ring $R$ is t-unital if the natural map $R\otimes_RR\rightarrow R$ is an isomorphism, and a left $R$-module $P$ is c-unital if the natural map $P\rightarrow\operatorname{Hom}_R(R,P)$ is an isomorphism. For a t-unital ring $R$,…

We introduce a cohomology theory that classifies differential objects that arise from Picard-Vessiot theory, using the differential Hopf-Galois descent. To do this, we provide an explicit description of Picard-Vessiot theory in terms of…

In this paper, a symplectic structure on a Leibniz algebra is defined to be a {\em symmetric} nondegenerate bilinear form satisfying certain compatibility condition, and a phase space of a Leibniz algebra is defined to be a symplectic…

For a cluster algebra $\mathcal{A}$ over $\mathbb{Q}$ of geometric type, a $\textit{frieze}$ of $\mathcal{A}$ is defined to be a $\mathbb{Q}$-algebra homomorphism from $\mathcal{A}$ to $\mathbb{Q}$ that takes positive integer values on all…

We investigate properties of varieties of algebras described by a novel concept of equation that we call \emph{commutator equation}. A commutator equation is a relaxation of the standard term equality obtained substituting the equality…

We investigate finitary functions from $\mathbb{Z}_{n}$ to $\mathbb{Z}_{n}$ for a squarefree number $n$. We show that the lattice of all clones on the squarefree set $\mathbb{Z}_{p_1\cdots p_m}$ which contain the addition of…

We study the algebras of derivations of nilpotent Leibniz algebras of low dimensions.

Based on work presented in [4], we define $S^2$-Upper Triangular Matrices and $S^2$-Lower Triangular Matrices, two special types of $d\times d(2d-1)$ matrices generalizing Upper and Lower Triangular Matrices, respectively. Then, we show…

We established two-sided Curto-Herrero conjecture for pairs of matrices, where the first matrix has a simple spectrum. Namely, it is shown that these pairs are separated by ranks of non-commutative polynomials in matrices. Moreover, we…