广义循环布尔矩阵三明治半群的正则元

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

设B={0,1}是二元布尔代数,Cn(r)是B上所有n阶r—循环矩阵组成之集,Gn=∪n-1r=0Cn(r),则Gn对二元布尔矩阵的乘法构成一个半群,称它为广义循环布尔矩阵半群.对于半群Gn中任一个固定的非零c—循环矩阵C,在Gn中定义一个新的运算“”如下:A,B∈Gn,AB=ACB.则(Gn,)也构成一个半群,称(Gn,)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Gn(C).本研究刻画了半群Gn(C)中的所有正则元,并且给出求Gn(C)中每一个正则元的所有g-逆的一个方法.

Let n be a Boolean algebra B = positive integer, and Cn （r） be the set of all B={0,1}, Gn=∪r=0^n-1 Cn（r）.Foranyfixed Cin trio n ×n r - circulant matrices over the Gn. We can define an operation＂ ＊ ＂ in Gn as follows： A ＊ B = ACB for any A, B in Gn, where ACB is the usual product of Boolean matrics. Then （Gn, ＊ ） is a semigroup which is called the sandwich semigroup of generalized circulant Boolean matrices with sandwich matrix C and denoted by Gn （ C）. In this paper, the regular elements in Gn （C） are characterized and an algorithm to determine all g - inverses for each regular element in Gn （C） is given.