局部环上n阶矩阵的{1}-逆作成的集合及其特征性质

Set of Some{1}-Inverse of an n×n Matrix and Its Characteristic Properties Over a Local Ring

运用有单位元的可换局部环上的矩阵广义逆理论和矩阵方法,研究了该局部环上一个可相似对角化的n阶矩阵A的某些{1}-逆构成的集合AP{1}及其扩集AP{1}∪{I},得到了集合AP{1}中元素的逆元存在的条件及扩集AP{1}∪{I}的子集作成子半群的条件.进一步地,还得到了集合AP{1}中元素的线性组合仍为{1}-逆的特征性质.

By the methods of matrix and theory of generalized Inverse matrix over a commutative local ring with an identity,the subsets of the set AP{1}and the set AP{1}∪{I}are discussed over the local ring,and the existential conditions of inverse elements of elements in AP{1}and the conditions which some special subsets of the set AP{1}∪{I}are semi-groups are given.Furthermore,some characteristic properties which linear combinations of elements in the set AP{1}still be{1}-Inverses of the matrix Aare obtained.