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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (10): 55-62.doi: 10.6040/j.issn.1671-9352.0.2019.636

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有限弱Y-稳定变换半群的极大子半群

金久林1,腾文1,2,祝富洋1,游泰杰1*,瞿云云1   

  1. 1.贵州师范大学数学科学学院, 贵州 贵阳 550001;2.贵州财经大学数学与统计学院, 贵州 贵阳 550025
  • 出版日期:2020-10-20 发布日期:2020-10-07
  • 作者简介:金久林(1991— ), 男, 博士研究生, 研究方向为信息代数、半群代数及其应用. E-mail:JinJiuLin2016@163.com*通信作者简介:游泰杰(1959— ), 男, 硕士, 教授, 博士生导师, 研究方向为信息代数、半群代数及其应用. E-mail:youtaijie1111@163.com
  • 基金资助:
    贵州省一流建设学科计划资助项目(C420001);贵州省科学技术基金资助项目(黔科合基础［2019］1221号)

Maximal subsemigroups of the finite transformation semigroup of weak Y-stabilizer

JIN Jiu-lin1, TENG Wen1,2, ZHU Fu-yang1, YOU Tai-jie1*, QU Yun-yun1   

  1. 1. School of Mathematics Science, Guizhou Normal University, Guiyang 550001, Guizhou, China;
    2. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, Guizhou, China
  • Online:2020-10-20 Published:2020-10-07

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摘要： 设X是一个非空集合,T(X)是X上的全变换半群。对X的任意非空子集Y,令T(X,Y)={α∈T〓(X):Yα⊆Y},称其为弱Y-稳定变换半群。当X为有限集且Y是X的非单点真子集时,给出了T(X,Y)的极大子半群的结构与完全分类。

关键词: 变换半群, 弱Y-稳定, 极大子半群

Abstract: Let X be a non-empty set. Denote by T (X)the full transformation semigroup on X. Given a non-empty subset Y of X, letT(X,Y)={α∈T (X):Yα⊆Y}, and call it the transformation semigroup of weak Y-stabilizer. In this paper, we show that structure and complete classification of maximal subsemigroups of T(X,Y)whenever Y is a proper non-singleton subset of finite set X.

Key words: transformation semigroup, weak Y-stabilizer, maximal subsemigroup

中图分类号: 

  • O152.7
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