Clifford矩阵半群

Clifford Semigroups of Matrices

运用Clifford半群中格林关系的特殊性,结合一些矩阵在一定条件下可同时对角化的方法,研究了任意数域上的矩阵构成的Clifford半群的结构,给出了Clifford矩阵半群中格林D类的一些一般刻画,并完全刻画了低阶矩阵构成的Clifford矩阵半群的结构,最后从已知的Clifford矩阵半群出发构造了一类新的Clifford矩阵半群.

We use the Greens’ relations on Clifford semigroups and combine the method of diagonalizing ma-trices under a number of certain conditions to study the structure of Clifford semigroups of matrices,character-ize generally the D-classes of these semigroups,and determine thoroughly the structure of the Clifford semig-roups of matrices of lower orders.Also we construct a kind of new Clifford semigroups of matrices from a given Clifford semigroup of matrices.