半群I_(n,r)的极大(完全)独立子半群  

MAXIMAL(COMPLETELY)ISOLATEDSUBSEMIGROUPS OF SEMGROUP I_(n,r)

作　　者：罗永贵 余江慧 肖坚 Luo Yonggui;Yu Jianghui;Xiao Jian(School of Mathematical Sciences,Guizhou Normal University,550025,Guiyang,China)

机构地区：[1]贵州师范大学数学科学学院,贵阳550025

出　　处：《山东师范大学学报（自然科学版）》2023年第2期122-128,共7页Journal of Shandong Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11861022);贵州师范大学学术新苗基金资助项目(黔师新苗[2021]B08号)。

摘　　要：设I_(n)和S_(n)分别是有限集X_(n)={1,2,…,n}上的对称逆半群和对称群.对0≤r≤n,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.对0≤r≤n-1,再令I_(n,r)=S_(n)UI(n,r),则I_(n,r)是对称逆半群I_(n)的子半群.为了研究半群I_(n,r)的极大(完全)独立子半群的完全分类,本文分析了半群I_(n,r)的格林关系及生成关系.首先,获得了半群I_(n,r)的(完全)独立子半群的完全分类;其次,确定了半群I_(n,r)的极大(完全)独立子半群的完全分类;最后,证明了半群I_(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,put I_(n,r)={α∈I_(n):imα≤r},then the I(n,r) are the two-sided ideals of I_(n).For 0≤r≤n-1,put I_(n,r)=S_(n)∪I(n,r),then the I(n,r) are the subsemigroups of I_(n).In order to study complete classification of the maximal(completely)isolated subsemigroups of I_(n,r),the Green′s relation and generation of I_(n,r) are analyzed.Firstly,the complete classification of the(completely)isolated subsemigroups of I_(n,r) is obtained.Secondly,the complete classification of the maximal(completely)isolated subsemigroups of I_(n,r) is determined.Finally,the coincide of maximal isolated subsemigroups and maximal completely isolated subscemigroups of I_(n,r) be proved.

关 键 词：对称逆半群 对称群 生成关系 极大独立子半群 极大完全独立子半群 

分 类 号：O152.7[理学—数学]