半群PHn的每个星理想的秩和幂等元秩

J4 ›› 2013, Vol. 48 ›› Issue (2): 42-48.

半群PHn的每个星理想的秩和幂等元秩

罗永贵,徐波,游泰杰

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:2012-03-20 出版日期:2013-02-20 发布日期:2013-03-04
作者简介:罗永贵(1985- ), 男, 硕士, 助教, 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(2009)02号); 贵州省科学技术基金资助项目(黔科合J字LKS(2011)16号)

On the rank and idempotent rank of each star ideal of the semigroup PHn

LUO Yong-gui, XU Bo, YOU Tai-jie

Department of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, Guizhou, China

Received:2012-03-20 Online:2013-02-20 Published:2013-03-04

摘要/Abstract

摘要：

设自然数n≥3, PHn是自然序集Xn=｛1,2,3,…,n｝上的保降序且保序有限部分奇异变换半群, 对0≤r≤n-1时, 记P(n,r)=｛α∈PHn:|imα|≤r｝为半群PHn的双边星理想。通过对其幂等元的分析, 分别刻划了半群P(n,r)的极小幂等生成集, 秩和幂等元秩。进一步证明了当0≤l≤r时, 半群P(n,r)关于它的每个星理想P(n,l)的相关秩。

关键词: 保降序; 保序; 奇异变换半群; 秩和幂等元秩; 相关秩

Abstract:

Let PHn be the semigroups of order-decreasing and orderpreserving finite partial singular transformations on the natural order set Xn=｛1,2,3,…,n｝ if n≥3, and let P(n,r)=｛α∈PHn:|imα|≤r｝ be the two-sided star ideal of the semigroup PHn if 0≤r≤n-1. By analyzing the idempotent elements, the minimal idempotent generating set, rank and idempotent rank of the semigroup P(n,r) are characterized, respectively. Furthermore, it is shown that for 0≤l≤r, the relative rank of the semigroup P(n,r) with respect to itself each star ideal P(n,l).

Key words: order-decreasing; order-preserving; singular transformation semigroup; rank and idempotent rank; relative rank

罗永贵,徐波,游泰杰. 半群PHn的每个星理想的秩和幂等元秩[J]. J4, 2013, 48(2): 42-48.

LUO Yong-gui, XU Bo, YOU Tai-jie. On the rank and idempotent rank of each star ideal of the semigroup PHn[J]. J4, 2013, 48(2): 42-48.

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