矩阵单逆半群

Simple Inverse Semigroups of Matrix

通过矩阵对角化的方法证明了矩阵单逆半群实际上是一个矩阵群及矩阵0-单逆半群在零元为素元时实际上是0-群,并通过Rees矩阵完全0-单逆半群,证明了一个矩阵半群是完全0-单逆半群的充分必要条件为其同构于平凡群对应的Brandt半群Bn。

The authors proved that a simple inverse semigroup of a matrix is actually a group of a matrix by the method of matrix diagonalization;a 0-simple inverse semigroup of a matrix is actually a 0-group when the zero is a prime element;and a semigroup of matrix is a completely 0-simple inverse semigroup if and only if it is isomorphic to the brandt semigroup Bn which the trivial group corresponds to by characterizing complete 0-simple inverse semigroups of matrix via Rees construction.