环与代数
We study ideal-simple commutative semirings and summarize the results giving their classification, in particular when they are finitely generated. In the principal case of (para)semifields, we then consider their minimal number of…
We introduce a class of graphs with coloured edges to encode subsystems of the classical root systems, which in particular classify them up to equivalence. We further use the graphs to describe root-kernel intersections, as well as…
We determine the $\sigma$-derivations of quantum tori and quantum affine spaces for a toric automorphism $\sigma$. By standard results, every toric automorphism $\sigma$ of a quantum affine space $\mathcal{A}$ and every $\sigma$-derivation…
Let ${\mathcal X} = (X, \{R_i\}_{i=0}^d)$ denote a symmetric association scheme. Fix an ordering $\{E_i\}_{i=0}^d$ of the primitive idempotents of $\mathcal{X}$, and let $P$ (resp.\ $Q$) denote the corresponding first eigenmatrix (resp.\…
In this paper we introduce the $r$-equilibrium problem and discuss connections to the map $det^{S^r}$. The case $r=2$ is an application of Newton's third law of motion, while $r=3$ deals with equilibrium of torque-like forces.
Halidon rings are rings with a unit element, containing a primitive $m^{th}$ root of unity and $m$ is invertible in the ring. The field of complex numbers is a halidon ring with any index $ m \geq 1$. In this article, the author examines…
The group scheme of ternary automorphisms of a perfect finite dimensional evolution algebra A is computed. The main advantage of using group schemes is that it allows to apply the Lie functor to determine the Lie algebra of ternary…
We systematically study those rings whose non-units are a sum of an idempotent and a nilpotent. Some crucial characteristic properties are completely described as well as some structural results for this class of rings are obtained. This…
On a finite structure, the polymorphism invariant relations are exactly the primitively positively definable relations. On infinite structures, these two sets of relations are different in general. Infinitary primitively positively…
We explicitly construct two-sided tilting complexes corresponding to Membrillo-Hern\'{a}ndez's tree-to-star tilting complexes for generalized Brauer tree algebras.
Let $R$ be a ring with identity and $\delta(R)$ denote the Zhou radical of $R$. A ring $R$ is called {\it $\delta$-reversible} if for any $a$, $b \in R$, $ab = 0$ implies $ba \in \delta(R)$. In this paper, we give some properties of…
We prove that the image of the total power operation for Burnside rings $A(G) \to A(G\wr\Sigma_n)$ lies inside a relatively small, combinatorial subring $\mathring A(G,n) \subseteq A(G \wr \Sigma_n)$. As $n$ varies, the subrings $\mathring…
This is the second paper in our series of papers dedicated to the study of maps on the mirror Heisenberg-Virasoro algebra. The first paper is dedicated to the study of unary maps and the present paper is dedicated to the study of binary…
The well-known Bachmuth-Mochizuki-Roman'kov Theorem \cite{BM,Romankov85} states that every automorphism of the free metabelian group of rank $\geq 4$ is tame. In 1992 Yu. Bahturin and S. Nabiyev \cite{BN} claimed that every nontrivial inner…
Some variations of $\pi$-regular and nil clean rings were recently introduced in \cite{5,8,7}, respectively. In this paper, we examine the structure and relationships between these classes of rings. Specifically, we prove that $(m,…
In this paper, we study the connectedness of the commuting graph of a general Lie algebra and provide a process to determine whether the commuting graph is connected or not, as well as to compute an upper bound for its diameter. In…
In this study, we aim to introduce the concept of classical 1-absorbing prime submodules of a nonzero unital module $M$ over a commutative ring $A$ with unity. A proper submodule $P$ of $M$ is said to be a classical 1-absorbing prime…
The aim of this short note is to prove the formula of the Hilbert series of the preprojective algebras in arbitrary characteristic by making effective use of the formulas of the Hilbert series of differential graded (dg) algebras with Adams…
In this paper, we consider compatible Hom-Leibniz algebra where the Hom map twists the operations in the compatible system. We consider a suitably graded Lie algebra whose Maurer-Cartan elements characterize the structure of compatible…
This paper studies the abelian subalgebras and ideals of maximal dimension of Poisson algebras $\mathcal{P}$ of dimension $n$. We introduce the invariants $\alpha$ and $\beta$ for Poisson algebras, which correspond to the dimension of an…