局部环上一类矩阵广义逆的偏序

Partial Ordering of Generalized Inverse of Classes Matrices over a Local Ring

设R是局部环,A=P-1(I(r)D)P∈Mn(R),其中D=diag{d1,…,dn-r}或D=0,d1,…,dn-r∈M,.研究R上集合意义下广义逆的矩阵偏序A≤[3]和A≤[2,3],确定了具有偏序A≤[3]和A≤[2,3]的矩阵集Mn(B┇A≤[3]B)和Mn(B┇A≤[2,3]B)都不是单点集.

Let R is a local ring,and A=P-1（I^（r）＋D）P in Mn（R）,where D=diag{d1,…,dn-r} or D=0,and d1,…,dn-r in M.In this paper,the partial ordering of generalized inverse of the classes matrices are discussed over a local ring,such as A≤^{3}B and A≤^{2,3}B;and the fact was given that the set Mn（B┇A≤^{3}B） and the set Mn（B┇A≤^{2,3}B） with the relations A≤^{3}B and A≤^{2,3}B both are not the set of the simple points.