摘要
设I n和S n分别为有限集X_(n)={1,2,…,n}上的对称逆半群和对称群.对0≤r≤n-1,令I(n,r)={α∈I n:|im(α)|≤r},则I(n,r)是对称逆半群I n的双边理想.记B_(n)=〈δ_(n)〉,其中对任意的i∈X_(n)有iδ_(n)=n+1-i,称B_(n)为X_(n)上的循环群.通过分析半群BI(n,r)=I(n,r)∪B_(n)的格林关系及生成关系,获得了半群BI(n,r)的(完全)独立子半群的完全分类.进一步,证明了半群BI(n,r)的极大独立子半群与极大完全独立子半群是一致的.
Let I n and S n be symmetric inverse semigroup and symmetric group on the finite set X_(n)={1,2,…,n},respectively.For 0≤r≤n-1,put I(n,r)={α∈I n:|im(α)|≤r},then the I(n,r)is a two-sided ideals of symmetric inverse semigroup I n.Denote B_(n)=〈δ_(n)〉,where there is iδ_(n)=n+1-i for any i∈X_(n),saying that B_(n)is a circle group on X_(n).By analyzing the Green’s relation and generative relation of the semigroup BI(n,r)=I(n,r)∪B_(n),the complete classification of the(completely)isolated subsemigroups of BI(n,r)is obtained.Furthermore,the coincide of maximal isolated subsemigroups and maximal completely isolated subsemigroups of BI(n,r)be proved.
作者
罗永贵
肖坚
余江慧
LUO Yong-gui;XIAO Jian;YU Jiang-hui(College of Mathematical Sciences,Guizhou Normal University,Guiyang 550025,China)
出处
《兰州理工大学学报》
北大核心
2025年第3期156-160,共5页
Journal of Lanzhou University of Technology
基金
国家自然科学基金(11861022)。
关键词
对称逆半群
对称群
循环群
(完全)独立子半群
极大(完全)独立子半群
symmetric inverse semigroup
symmetric group
circle group
(compeletly)isolated subsemigroups
the maximal(completely)isolated subsemigroups
