浙江大学学报（理学版）
浙江大學學報（理學版）
절강대학학보（이학판）
JOURNAL OF ZHEJIANG UNIVERSITY
2011年
5期
489-494
,共6页
广义循环布尔矩阵%三明治半群%完全正则元
廣義循環佈爾矩陣%三明治半群%完全正則元
엄의순배포이구진%삼명치반군%완전정칙원
generalized circulant Boolean matrix%sandwich semigroup%fully regular element
设n是一个正整数,Gn(r)是B={0,1}上所有n阶r-循环矩阵组成之集,Gn=n-1∪r=0(r).对于半群Gn中任一个固定的r循环矩阵C,在Gn中定义一个新的运算“*”:(V)A,B∈Gn,A* B=ACB.则(Gn,*)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).刻画了半群Gn(C)中的完全正则元,并给出了求Gn(C)中所有完全正则元的算法.
設n是一箇正整數,Gn(r)是B={0,1}上所有n階r-循環矩陣組成之集,Gn=n-1∪r=0(r).對于半群Gn中任一箇固定的r循環矩陣C,在Gn中定義一箇新的運算“*”:(V)A,B∈Gn,A* B=ACB.則(Gn,*)構成一箇半群,稱(Gn,*)為(帶有三明治矩陣C的)廣義循環佈爾矩陣三明治半群,併記為Gn(C).刻畫瞭半群Gn(C)中的完全正則元,併給齣瞭求Gn(C)中所有完全正則元的算法.
설n시일개정정수,Gn(r)시B={0,1}상소유n계r-순배구진조성지집,Gn=n-1∪r=0(r).대우반군Gn중임일개고정적r순배구진C,재Gn중정의일개신적운산“*”:(V)A,B∈Gn,A* B=ACB.칙(Gn,*)구성일개반군,칭(Gn,*)위(대유삼명치구진C적)엄의순배포이구진삼명치반군,병기위Gn(C).각화료반군Gn(C)중적완전정칙원,병급출료구Gn(C)중소유완전정칙원적산법.
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.
