arXiv subjects

Henrique Guzzo Jr.

Publications and source records attributed to Henrique Guzzo Jr..

5 recordsLinked to original sources

arXiv2025

On the additivity of n-multiplicative isomorphisms, derivations, and related maps in axial algebras

In this paper, we demonstrate that several classes of functions, specifically n-multiplicative isomorphisms, derivations, elementary maps, and Jordan elementary maps on a class of algebras that includes Jordan algebras with idempotents, J(a)-axial algebras and M(a,b)-axial algebras, are additive under appropriate conditions, which may be referred to as Martindale-type conditions. Furthermore, we answer the question left open in the recent article titled "Multiplicative isomorphisms and derivations on axial algebra."

math.RA↗

arXiv2021

On simple $15$-dimensional Lie algebras in characteristic $2$

Motivated by the recent progress towards classification of simple finite-dimensional Lie algebras over an algebraically closed field of characteristic $2$, we investigate such $15$-dimensional algebras.

math.RA↗

arXiv2020

Lie maps on alternative rings preserving idempotents

Let $\Re$ and $\Re'$ unital $2$,$3$-torsion free alternative rings and $φ: \Re \rightarrow \Re'$ be a surjective Lie multiplicative map that preserves idempotents. Assume that $\Re$ has a nontrivial idempotents. Under certain assumptions on $\Re$, we prove that $φ$ is of the form $ψ+ τ$, where $ψ$ is either an isomorphism or the negative of an anti-isomorphism of $\Re$ onto $\Re'$ and $τ$ is an additive mapping of $\Re$ into the centre of $\Re'$ which maps commutators into zero.

math.RA↗

arXiv2020

Multiplicative Lie-type derivations on alternative rings

Let $\R$ be an alternative ring containing a nontrivial idempotent and $\D$ be a multiplicative Lie-type derivation from $\R$ into itself. Under certain assumptions on $\R$, we prove that $\D$ is almost additive. Let $p_n(x_1, x_2, \cdots, x_n)$ be the $(n-1)$-th commutator defined by $n$ indeterminates $x_1, \cdots, x_n$. If $\R$ is a unital alternative ring with a nontrivial idempotent and is $\{2,3,n-1,n-3\}$-torsion free, it is shown under certain condition of $\R$ and $\D$, that $\D=δ+τ$, where $δ$ is a derivation and $τ\colon\R\longrightarrow{\mathcal Z}(\R)$ such that $τ(p_n(a_1,\ldots,a_n))=0$ for all $a_1,\ldots,a_n\in\R$.

math.RA↗

arXiv2018

Generalized Jordan derivations on semiprime rings

The purpose of this note is to prove the following. Suppose $\R$ is a semiprime unity ring having an idempotent element e $\left(e \neq 0, e \neq 1\right)$ which satisfies mild conditions. It is shown that every additive generalized Jordan derivation on $\R$ is a generalized derivation.

math.RA↗