局部环上n阶矩阵的{1}-逆作成的群  

Groups of {1}-inverses of matrix Aof order nover a local ring

作　　者：吴炎[1] 杨其强[1] 

机构地区：[1]琼州学院理工学院,海南三亚572022

出　　处：《东北师大学报（自然科学版）》2014年第3期28-33,共6页Journal of Northeast Normal University(Natural Science Edition)

基　　金：海南省自然科学基金资助项目(113008)

摘　　要：研究了有单位元的可换局部环上n阶可对角化的矩阵A的{1}-逆集中的子群及其构造问题,运用矩阵和群方法,给出了这个矩阵A的{1}-逆集AP{1}-中元素的乘法封闭的条件,获得了矩阵A的{1}-逆集AP{1}中的子集作成群的充要条件,以及这些子群的结构定理及相关结果.In this paper, we study the subgroups of the set Ap {1} formed by some { 1 }-inverses ofdiagonalization matrix A of order n over a commutative local ring with an identity and their structures.By using the methods of matrix and group,we give the conditions on the closure of multiplication inthe set Ae { 1}. Furthermore, we also obtain some necessary and sufficient conditions that make thesubsets of the set Ae { 1 } into groups and some structure theorems about these subgroups and somerelevant results.

关 键 词：可换局部环 广义逆矩阵 矩阵群 LU分解 

分 类 号：O151.21[理学—数学]