交换环上严格上三角矩阵半群的自同构

摘要

设R是任意含有单位元的交换环，Nn（R）是R上的所有n×n严格上三角矩阵组成的乘法半群．本文对Nn（R）的任意自同构给出了详细的描述．%Let R be an arbitrary commutative ring with identity, and Nn（R） be the multiplicative semigroup consisting of all n × n strictly upper triangular matrices over R. The aim of this paper is to give an explicit description of any automorphism of the semigroup Nn （R）. Key words： semigroup; automorphism; strictly upper triangular matrix; commutative ring