可换环上上三角矩阵代数的局部若当导子和局部若当自同构

Local Jordan Derivations and Local Jordan Automorphisms of Upper Triangular Matrix Algebras

中文关键词:  局部若当导子  局部若当自同构  局部导子  局部自同构  上三角矩阵代数.

英文关键词:local Jordan derivations  local Jordan automorphisms  local derivations  local automorphisms  upper triangular matrix algebras.

中文摘要:

      设$R$是含有单位元的可换环,$T_{n}(R)$表示$R$上所有$n\times n$级上三角矩阵所形成的$R-$代数.本文证明了$T_{n}(R)$的每一个局部若当导子都是内导子,$T_{n}(R)$的每一个局部若当自同构都是若当自同构.作为应用,同时也证明了$T_{n}(R)$的局部导子和局部自同构分别是内导子和内自同构.

英文摘要:

      Let $R$ be a commutative ring with identity, $T_{n}(R)$ the $R$-algebra of all upper triangular $n$ by $n$ matrices over $R$. In this paper, it is proved that every local Jordan derivation of $T_{n}(R)$ is an inner derivation and that every local Jordan automorphism of $T_{n}(R)$ is a Jordan automorphism. As applications, we show that local derivations and local automorphisms of $T_{n}(R)$ are inner.