广义循环布尔矩阵三明治半群中的完全正则元

设n是一个正整数, Cn(r)是B={0,1}上所有n阶r 循环矩阵组成之集, Gn=∪〖DD(〗n－1〖〗r=0〖DD)〗Cn(r). 对于半群Gn中任一个固定的r 循环矩阵C,在Gn中定义一个新的运算“*”：A,B∈Gn, AB=ACB. 则(Gn,)构成一个半群, 称(Gn,)为（带有三明治矩阵C的）广义循环布尔矩阵三明治半群, 并记为Gn(C).刻画了半群Gn(C)中的完全正则元,并给出了求Gn(C)中所有完全正则元的算法.

The fully regular elements of the sandwich semigroup of generalized circulant Boolean matrices

Let n be a positive integer,and Cn (r) be the set of all n × n r-circulant matrices over the Boolean algebra B ={0,1},Gn=n-1∪r=0 Cn(r).For any fixed r-circulant matrix C(C≠0) in Gn.Define an operation “ * ” in Gn:A * B=ACB for any A,B in Gn,where ACB is the usual product of Boolean matrices.Then (Gn,* ) is a semigroup.We denote this semigroup by Gn (C) and call it the sandwich semigroup of generalized circulant Boolean matrices with sandwich matrix C.In this paper,the fully regular elements in Gn (C) are characterized.The algorithm to find all the fully regular elements of A in Gn (C) is given.