arXiv subjects
Publications and source records attributed to Bruno L. M. Ferreira.
Let A and A' be two alternative *-algebras with identities 1_A and 1_A', respectively, and e_1 and e_2 = 1_A - e_1 nontrivial symmetric idempotents in A. In this paper we study the characterization of multiplicative *-Jordan-type maps on alternative algebras.
Let $\mathfrak{R}$ and $\mathfrak{R}'$ be two associative rings (not necessarily with the identity elements). A bijective map $φ$ of $\mathfrak{R}$ onto $\mathfrak{R}'$ is called a \textit{$m$-multiplicative isomorphism} if {$φ(x_{1} \cdots x_{m}) = φ(x_{1}) \cdots φ(x_{m})$} for all $x_{1}, \cdots ,x_{m}\in \mathfrak{R}.$ In this article, we establish a condition on generalized $n$-matrix rings, that assures that multiplicative maps are additive on generalized $n$-matrix rings under certain restrictions. And then, we apply our result for study of $m$-multiplicative isomorphism and $m$-multiplicative derivation on generalized $n$-matrix rings.
Let $R$ be a ring with involution containing a nontrivial symmetric idempotent element $e$. Let $δ: R\rightarrow R$ be a mapping such that $δ(ab)=δ(b)a^{\ast}+b^{\ast}δ(a)$ for all $a,b\in R$, we call $δ$ a $\ast-$reverse derivable map on $R$. In this paper, our aim is to show that under some suitable restrictions imposed on $R$, every $\ast-$reverse derivable map of $R$ is additive.