局部环上矩阵模的保乘法自同态

THE ENDOMORPHISM PRESERVING MULTIPLI-CATION OF MATRIX OVER LOCAL RING

本文研究了局部环上矩阵模保乘法自同态,主要结果是:L是非零的保乘法自同态(?)存在P∈GL_n(R),使L(A)=P^(-1)AP,(?)A∈M_n(R)。

Let R be a commutative local ring with I in R, M_n(R) denotes the modules of nxn matrices over R. In this paper we proved following result:L is a nonzero endomorphism preserving multiplication if and only if there is a matrix Pin GL_n(R)such as L(A)=P^(-1)AP, (?)A∈M_n(R).