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山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (10): 7-11.doi: 10.6040/j.issn.1671-9352.0.2016.471

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半群W(n,r)的极大(正则)子半群

罗永贵   

  1. 贵州师范大学数学科学学院, 贵州 贵阳 550001
  • 收稿日期:2016-10-20 出版日期:2017-10-20 发布日期:2017-10-12
  • 作者简介:罗永贵(1985— ), 男, 硕士, 讲师, 研究方向为半群代数理论. E-mail:luoyonggui851010@hotmail.com
  • 基金资助:
    贵州省科学技术基金资助项目(黔科合LH字(2014)7056号)

Maximal(regular)subsemigroups of the semigroup W(n,r)

LUO Yong-gui   

  1. School of Mathematics Science, Guizhou Normal University, Guiyang 550001, Guizhou, China
  • Received:2016-10-20 Online:2017-10-20 Published:2017-10-12

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摘要： 设自然数n≥3, RWn是有限链［n］上的正则保序且压缩奇异变换半群。对任意的r(1≤r≤n-1), 记W(n,r)={α∈RWn:|Im(α)|≤r}为半群RWn的双边理想。通过对秩为r的元素和格林关系的分析, 获得了半群W(n,r)的极大(正则)子半群的完全分类。

关键词: 奇异变换半群, 完全分类, 正则压缩, 保序, 极大(正则)子半群

Abstract: Let RWn be the semigroup of all regular order-preserving and compressing singular transformations on a finite-chain［n］ if n≥3, and let W(n,r)={α∈RWn:|Im(α)|≤r} be the two-sided ideal of the semigroup RWn for an arbitrary integer r accord with 1≤r≤n-1. By analyzing the elements of rank r and Greens relations, the classification of the maximal(regular)subsemigroup of the semigroup W(n,r) is completely obtained.

Key words: regular compression, order-preserving, maximal(regular)subsemigroup, singular transformation semigroup, complete classification

中图分类号: 

  • O152.7
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