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《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (12): 19-24.doi: 10.6040/j.issn.1671-9352.0.2020.319

• • 上一篇    

半群H *(n,m)(r)的极大子半群与极大正则子半群

袁月,赵平*   

  1. 贵州师范大学数学科学学院, 贵州 贵阳 550025
  • 发布日期:2020-12-01
  • 作者简介:袁月(1995— ), 女, 硕士研究生, 研究方向为半群理论. E-mail:15110565999@163.com*通信作者简介:赵平(1973— ), 男, 教授, 博士生导师, 研究方向为半群理论. E-mail:pingzhao731108@163.com
  • 基金资助:
    贵州师范大学2019年博士科研启动项目(GZNUD［2019］13号)

Maximal subsemigroups and the maximal regular subsemigroups of the semigroup H *(n,m)(r)

YUAN Yue, ZHAO Ping*   

  1. School of Mathematics Science, Guizhou Normal University, Guiyang 550025, Guizhou, China
  • Published:2020-12-01

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摘要： 设Tn是Xn={1,2,…,n}上的全变换半群,对任意1≤m≤n-1,记Xm={1,2,…,m}。通过半群T(n,m)={α∈Tn:Xmα=Xm} 的子半群G(n,m)={α∈T(n,m):(Xn\Xm)α=Xn\Xm}和H(n,m)={α∈T(n,m):(Xn\Xm)α⊆Xn\Xm},对1≤m*(n,m)(r)={α∈H(n,m):|im(α)|≤r}∪G(n,m)的子半群, 证明了H *(n,m)(r)的极大子半群和极大正则子半群是一致的。

关键词: 全变换半群, 对称群, 等价关系, 极大正则子半群, 极大子半群

Abstract: Let Tn be the full transformation semigroup on Xn={1,2,…,n}. For any 1≤m≤n-1, let Xm={1,2,…,m}. Through the subsemigroupsG(n,m)={α∈T(n,m):(Xn\Xm)α=Xn\Xm}andH(n,m)={α∈T(n,m):(Xn\Xm)α⊆Xn\Xm}of the semigroup T(n,m)={α∈Tn:Xmα=Xm}, the subsemigroups of the semigroup H *(n,m)(r)={α∈H(n,m):|im(α)|≤r}∪G(n,m) are studied for 1≤m1, and it is proved that the maximal subsemigroups of H *(n,m)(r)are the same as the maximal regular subsemigroups.

Key words: full transformation semigroup, symmetric group, equivalence relation, maximal regular subsemigroup, maximal subsemigroup

中图分类号: 

  • O152.7
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