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浙江大学学报(理学版)  2011, Vol. 38 Issue (5): 489-494    
数学与计算机科学     
广义循环布尔矩阵三明治半群中的完全正则元
The fully regular elements of the sandwich Semigroup of generalized circulant Boolean matrices
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摘要: 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.
Abstract: Let n be a positive integer, and Cn(r) be the set of all n×n rcirculant matrices over the Boolean algebra B={0,1}, Gn=∪〖DD(〗n-1〖〗r=0〖DD)〗Cn(r). For any fixed rcirculant matrix C(C≠0) in Gn. Define an operation “” in Gn∶AB=ACB for any A,B in Gn, where ACB is the usual product of Boolean matrices. Then (Gn,) is a semigroup. We denote this semigroup by Gn(C) and call it the sandwich semigroup of generalized circulant Boolean matrices with sandwich matrix C. In this paper, the fully regular elements in Gn(C) are characterized. The algorithm to find all the fully regular elements of A in Gn(C) is given.
出版日期: 2013-10-18
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