矩阵单逆半群  

Simple Inverse Semigroups of Matrix

作　　者：左落栗[1] 朱用文[1] 

机构地区：[1]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《吉林大学学报（理学版）》2010年第5期733-736,共4页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10571005)

摘　　要：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.

关 键 词：矩阵半群 逆半群 单半群 0-单半群 

分 类 号：O152.7[理学—数学]