环与代数
Motivated by recent advances in inverse semigroup theory, we investigate the growth of and identities satisfied by free left and free two-sided adequate monoids. We explicitly compute the growth of the monogenic free left adequate monoid…
In this paper we consider the algebra of upper triangular matrices UT$_n(F)$, endowed with a $\mathbb{Z}_2$-grading (superalgebra) and equipped with a superinvolution. These structures naturally arise in the context of Lie and Jordan…
The symmetric inverse monoid $I_X$ on a set $X$ consists of all bijective functions whose domain and range are subsets of $X$ under the usual composition and inversion of partial functions. For an arbitrary infinite set $X$, we classify all…
Transposed Poisson algebra was introduced as a dual notion of the Poisson algebra by switching the roles played by the commutative associative operation and Lie operation in the Leibniz rule defining the Poisson algebra. Let $H$ be a Hopf…
In 2025, Mosi\'{c} defined the weak CMP inverse utilizing a minimal rank weak Drazin inverse instead of the Drazin inverse. The weak CMP inverse is a new wider class of generalized inverses, of which the CMP and MPCEP inverse are particular…
We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.
We partially answer two questions of Goodaire by showing that in a finite, strongly right alternative ring, the set of units (if the ring is with unity) is a Bol loop under ring multiplication, and the set of quasiregular elements is a Bol…
The expected signature of a family of paths need not be a signature of a path itself. Motivated by this, we consider the notion of a Lie group barycenter introduced by Buser and Karcher to propose a barycenter on path signatures. We show…
This article investigates various notions of primeness for one-sided ideals in noncommutative rings, with a focus on principal ideal domains.
We explicitly describe the structure of HNN extensions of Lie superalgebras. We specify their bases. Moreover, we prove that the HNN extension is a direct sum of two subalgebras: original Lie superalgebra, and the free Lie superalgebra,…
By using the energy operator introduced by B. Bakalov, A. De Sole, and V.\,G. Kac, we propose an algorithm for computing the cohomology of finitely generated free Lie conformal algebras with a Virasoro element. This computational method…
In this paper, we introduce the concept of L-dendriform conformal algebras, which arise naturally from the study of $\mathcal{O}$-operators on left-symmetric conformal algebras and solutions to the conformal $S$-equation. These algebras…
In this paper, Ore extensions of multiplier Hopf coquasigroups are studied. Necessary and sufficient conditions for the Ore extension of a regular multiplier Hopf coquasigroup to be a multiplier Hopf coquasigroup are given. Furthermore, the…
Leibniz algebras are non-antisymmetric generalizations of Lie algebras that have attracted substantial interest due to their close relation with the latter class. A Leibniz algebra $A$ is called perfect if it coincides with its derived…
We establish noncommutative Kn\"{o}rrer periodicity for projective-module factorizations over an arbitrary ring, using the equivariantization theory with respect to various actions by a cyclic group of order two. We obtain an explicit…
In this paper, we introduce and explore in-depth the notion of {\it weakly strongly 2-nil-clean rings} as a common non-trivial generalization of both strongly 2-nil-clean rings and strongly weakly nil-clean rings as defined and studied by…
In this paper, we compute the Gr\"obner-Shirshov bases for certain regular double extension algebras by means of an algorithm implemented in Matlab, which facilitates the underlying algebraic computations. Moreover, we establish that these…
To the best of our knowledge, there is no explicit, constructive description of the generating set for the unit group $A(G)^\times$ of the Burnside ring associated with a finite group $G$. We resolve this long-standing open question,…
In this thesis we study the subsemigroup structure of the symmetric inverse monoid $I_X$, the inverse semigroup of bijections between subsets of the set $X$, when $X$ is an infinite set. We explore three different approaches to this task.…
Given a monoid $H$ (written multiplicatively), the family $\mathcal{P}_{\mathrm{fin},1}(H)$ of all non-empty finite subsets of $H$ containing the identity element $1_H$ is itself a monoid, called the reduced finitary power monoid of $H$,…