交换环上矩阵代数的局部化导子

Local Derivations of a Matrix Algebra over a Commutative Ring

中文关键词:  导子  局部化导子  R-代数

英文关键词:derivations  local derivations  $R$-algebras.

中文摘要:

      假设R是一个含幺交换环,Nn(R)是由R上所有n阶严格上三角矩阵组成的矩阵代数.当n≦4时我们构造了几种Nn(R)的真局部化导子(的显式表示),(由此我们得到重要的结论)基于这些真局部化导子,当n≦4及R是整域时,Nn(R)的所有局部化导子都能以显式形式表示.

英文摘要:

      Let $R$ be a commutative ring with identity, $N_n(R)$ the matrix algebra consisting of all $n\times n$ strictly upper triangular matrices over $R$. Several types of proper local derivations of $N_n(R)~(n\leq 4)$ are constructed, based on which all local derivations of $N_n(R)~(n\leq 4)$ are characterized when $R$ is a domain.