非交换主理想整环上三矩阵乘积的Moore-Penrose逆的倒换顺序律

The Reverse Order Law About the Moore-Penrose Inverse of the Product of Three Motrices Over a Non-Commutative PID

本文研究非交换主理想整环R上三矩阵乘积M-P逆的倒序律成立的刻划问题文中阐述R上矩阵的秩的定义,并利用R上矩阵与 R所嵌入的商除环K上矩阵的秩之间的关系,把文[2]中复矩阵的主要结果直至推广到R上,得到了倒序律成立的若干个刻划.

This paper studies characterzation, for the reverse order law about the Moore-Peuro.se inverse of product of three matrices over a non-commutative principal ideal domain R, and generalized the results of matrices over the complex field to R.