局部环上矩阵广义逆半群的子集及其性质

Subsets of Generalized Inverse Matrices Semigroup of a n×n Matrix a and Their Properties over a Local Ring

设R是一个局部环,A是一个可相似对角化的n阶矩阵.利用矩阵方法研究了环R上矩阵A的广义逆半群的子集,得到了其做成正规子群的条件和其中元素可逆的条件,也得到了矩阵广义逆半群的一些性质.

Let Ris a local ring, and let matrix A is an n×n similar diagonalization matrix over R. In this paper, by the matrix methods over local rings, we discuss some subsets of the generalized inverse matrices semigroup about a n×n matrix A with entries from R, and obtain the conditions about elements is invertihle in these subsets and the conditions of the subsets are the normal groups ,and give some properties of the generalized inverse matrices semigroup.