半群W(n,r)的非群元秩和相关秩

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

半群W(n,r)的非群元秩和相关秩

罗永贵

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

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/Abstract

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

罗永贵. 半群W(n,r)的非群元秩和相关秩[J]. J4, 2013, 48(12): 70-74.

LUO Yong-gui. Non-group rank and relative rank of the semigroup W(n,r)[J]. J4, 2013, 48(12): 70-74.

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