论文标题
广义n矩阵环上的乘法图
Multiplicative Maps on Generalized n-matrix Rings
论文作者
论文摘要
令$ \ mathfrak {r} $和$ \ mathfrak {r}'$为两个关联戒指（不一定带有身份元素）。 $ \ mathfrak {r} $ of $ \ mathfrak {r}'$的$ \ mathfrak {r} $ $ \ textit {$ m $ -m $ -multiplicative Insomorphism}的beixtive图$φ$φ$φ$φ$φ$ $ \ mathfrak {r} $，如果{$φ（x__ {1} \ cdots x_ {m}）所有$ x_ {1}，\ cdots，x_ {m} \ in \ mathfrak {r}。$在本文中，我们在某些限制下对广义$ n $ -matrix环建立了条件，以确保多liquillicative映射对广义$ n $ -matrix戒指的添加剂。然后，我们将结果应用于$ M $ $ - 多态性同构和$ M $ $ M $ - 千年派生的衍生产品。
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.
