Related papers: Morphisms on $EMV$-algebras and Their Applications

This paper aims to establish a framework for extreme learning machines (ELMs) on general hypercomplex algebras. Hypercomplex neural networks are machine learning models that feature higher-dimension numbers as parameters, inputs, and…

The category $\bcalNT$ is a category of certain commutative graded algebras over a field. It was introduced in \cite{Lobos2} as a generalization of algebras generated by Jucys-Murphy elements in the many \textbf{End} algebras of the…

Classification, up to isomorphism, of algebras from a non-empty subset of the variety of $n$- dimensional algebras is presented. It is shown that these algebras have only trivial automorphism and if the basic field is algebraically closed…

An MV-module is an MV-algebra endowed with a scalar multiplication with scalars in a PMV-algebra (i.e. an MV-algebra endowed with a binary "ring-like" product). We investigate the class of semisimple MV-modules over a semisimple and totally…

This is a survey of recent progress in several areas of combinatorial algebra. We consider combinatorial problems about free groups, polynomial algebras, free associative and Lie algebras. Our main idea is to study automorphisms and, more…

We prove that any Bernstein algebra $(A, \omega)$ is isomorphic to a semidirect product $V \ltimes_{(\cdot, \, \Omega)} \, k$ associated to a commutative algebra $(V, \cdot)$ such that $(x^2)^2 = 0$, for all $x\in A$ and an idempotent…

We consider an orbit category of the bounded derived category of a path algebra of type A_n which can be viewed as a -(m+1)-cluster category, for m >= 1. In particular, we give a characterisation of those maximal m-rigid objects whose…

We consider homogeneous varieties of linear algebras over an associative-commutative ring K with 1, i.e., the varieties in which free algebras are graded. Let F be a free algebra of some variety A of linear algebras over K freely generated…

We introduce a class of monotone $\sigma$-complete effect algebras, called representable, which are $\sigma$-homomorphic images of a class of monotone $\sigma$-complete effect algebras of functions taking values in the interval $[0,1]$ and…

This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the…

In this paper we give a small review of some recent results of elementary equivalence of linear and algebraic groups and our last new results of elementary equivalence of categories of modules, endomorphism rings of modules, lattices of…

Last years a number of papers were devoted to describing automorphisms of semigroups of endomorphisms of free finitely generated universal algebras of some varieties: groups, semigroups, associative commutative algebras, inverse semigroups,…

Given an algebraic Lie algebra $\mathfrak{g}$ over $\mathbb{C}$, we canonically associate to it a Lie algebra $\mathfrak{g}_{\infty}$ defined over $\mathbb{C}_{\infty}$-the reduction of $\mathbb{C}$ mod infinitely large prime, and show that…

This paper studies the formal deformations of differential algebra morphisms. As a consequence, we develop a cohomology theory of differential algebra morphisms to interpret the lower degree cohomology groups as formal deformations. Then,…

First, we construct some families of nonsolvable anticommutative algebras, solvable Lie algebras and even nilpotent Lie algebras, that can be endowed with the structure of a simple Hom-Lie algebra. This situation shows that a classification…

We study algebraic conditions when a pseudo MV-algebra is an interval in the lexicographic product of an Abelian unital $\ell$-group and an $\ell$-group that is not necessary Abelian. We introduce $(H,u)$-perfect pseudo MV-algebras and…

Any variety of classical algebras has a so-called conformal counterpart. For example one can consider Lie conformal or associative conformal algebras. Lie conformal algebras are closely related to vertex algebras. We define free objects in…

Using the description of enriched $\infty$-operads as associative algebras in symmetric sequences, we define algebras for enriched $\infty$-operads as certain modules in symmetric sequences. For $\mathbf{V}$ a symmetric monoidal model…

We describe mutation elements in free $\mathfrak{perm}$ algebras. Moreover, we construct a base of free mutation of free $\mathfrak{perm}$ algebra. Using Cohn's criterion for the specialty of algebras, we show that there is an exceptional…

In this paper, we study the endomorphism properties of vertex operator algebras over an arbitrary field $\mathbb{F}$, with $\text{Char}(\mathbb{F}) \neq 2$. Let $V$ be a strongly finitely generated vertex operator algebra over $\mathbb{F}$,…