半群BI(n,r)的极大(完全)独立子半群

兰州理工大学学报 ›› 2025, Vol. 51 ›› Issue (3): 156-160.

半群BI(n,r)的极大(完全)独立子半群

罗永贵^*, 肖坚, 余江慧

贵州师范大学数学科学学院, 贵州贵阳 550025

收稿日期:2023-05-04 出版日期:2025-06-28 发布日期:2025-06-30
通讯作者: 罗永贵(1985-),男,贵州安顺人,副教授.Email:luoyonggui417@126.com
基金资助:
国家自然科学基金(11861022)

Maximal (completely) isolated subsemigroups of semigroup BI(n,r)

LUO Yong-gui, XIAO Jian, YU Jiang-hui

College of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China

Received:2023-05-04 Online:2025-06-28 Published:2025-06-30

摘要/Abstract

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.

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

Abstract: 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 i δ_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.

Key words: symmetric inverse semigroup, symmetric group, circle group, (compeletly) isolated subsemigroups, the maximal (completely) isolated subsemigroups

中图分类号:

O152.7

罗永贵, 肖坚, 余江慧. 半群BI(n,r)的极大(完全)独立子半群[J]. 兰州理工大学学报, 2025, 51(3): 156-160.

LUO Yong-gui, XIAO Jian, YU Jiang-hui. Maximal (completely) isolated subsemigroups of semigroup BI(n,r)[J]. Journal of Lanzhou University of Technology, 2025, 51(3): 156-160.

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