arXiv subjects
Publications and source records attributed to Aline Jaqueline de Oliveira Andrade.
In this paper, we address the additivity of $n$-multiplicative isomorphisms and $n$-multiplicative derivations on Gamma rings. We proved that, if $\M$ is a $Γ$-ring satisfying the some conditions, then any $n$-multiplicative isomorphism $\left(φ, ϕ\right)$ of $\M$ onto an arbitrary gamma ring is additive.
Let $A$ be an unital alternative $*$-algebra. Assume that $A$ contains a nontrivial symmetric idempotent element $e$ which satisfies $xA \cdot e = 0$ implies $x = 0$ and $xA \cdot (1_A - e) = 0$ implies $x = 0$. In this paper, it is shown that $Φ$ is a nonlinear $*$-Jordan-type derivation on A if and only if $Φ$ is an additive $*$-derivation. As application, we get a result on alternative $W^{*}$-algebras.