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J4 ›› 2013, Vol. 48 ›› Issue (12): 70-74.

• 论文 • 上一篇    下一篇

半群W(n,r)的非群元秩和相关秩

罗永贵   

  1. 贵州师范大学数学与计算机科学学院, 贵州 贵阳 550001
  • 收稿日期:2013-03-05 出版日期:2013-12-20 发布日期:2014-01-09
  • 作者简介:罗永贵(1985- ), 男, 讲师, 硕士,研究方向为半群代数理论. Email:luoyonggui851010@hotmail.com
  • 基金资助:

    贵州省科学技术基金资助项目(黔科合J字LKS(2011)15号)

Non-group rank and relative rank of the semigroup W(n,r)

LUO Yong-gui   

  1. Department of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, Guizhou, China
  • Received:2013-03-05 Online:2013-12-20 Published:2014-01-09

摘要:

设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(2≤r≤n-1),考虑半群W(n,r)={α∈RWn:|Imα|≤r}的非群元秩和非幂等元秩。证明了:W(n,r)是由秩为r的元素生成的;确定了当1≤l≤r时,半群W(n,r)关于其理想W(n,l)的相关秩。

关键词: 保序;压缩;奇异变换半群;非群元秩和非幂等元秩;相关秩

Abstract:

Let RWn be the semigroup of all regular order-preserving and compressing singular transformations on a finite-chain [n]. For an arbitrary integer r(2≤r≤n-1), the non-group rank and non-idempotent rank of the semigroup W(n,r)={α∈RWn:|Imα|≤r} were studied. The semigroup W(n,r) generated by elements of rank r is proved. Furthermore, it is shown that for 1≤l≤r, the relative rank of the semigroup W(n,r) with respect to itself each ideal W(n,l).

Key words: order-preserving; compression; singular transformation semigroup; non-group rank and non-idempotent rank; relative rank

中图分类号: 

  • O152.7
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