摘要
设X_n={1,2,…,n}为有限链,T_n是X_n上的全变换半群。给定k∈X_n,记W(n,k),R(n,k)分别为T_n的如下子集{f∈T_n:(x,y∈X_n),|x-k|≤|y-k|?|f(x)-k|≤|f(y)-k|},{f∈T_n:(x,y∈X_n),|x-k|≤|y-k|?|f(x)-k|≥||f(y)-k||}W(n,k)与R(n,k)的并集记作M(n,k)。显然,M(n,k)是T_n的子半群。讨论了半群M(n,k)的正则性并刻画了它的格林关系。
Let X n={1,2,…,n}be a finite chain and let T n be the full transformation semigroup on X n.Suppose that k is a fixed element of X n,denote by W(n,k)and R(n,k)the subsets of T n defined as{f∈Tn:(■x,y∈Xn),|x-k|≤|y-k|■|f(x)-k|≤|f(y)-k|},{f∈Tn:(■x,y∈Xn),|x-k|≤|y-k|■|f(x)-k|≥|f(y)-k|}respectively,and denote by M(n,k)the union of W(n,k)and R(n,k).Obviously,M(n,k)is a subsemigroup of T n.In this paper,we discuss the regularity of the semigroup M(n,k)and characterize its Green’s relations.
作者
袁新
徐波
YUAN Xin;XU Bo(School of Mathematics Science,Guizhou Normal University,Guiyang,Guizhou 550025,China)
出处
《贵州师范大学学报（自然科学版）》
CAS
2019年第1期65-68,共4页
Journal of Guizhou Normal University：Natural Sciences
基金
国家自然科学基金(NO:11461014)
关键词
变换半群
正则元
格林关系
order-preserving semigroup
regular element
Green's relations
