降序且保序有限部分变换半群的幂等元秩

J4 ›› 2011, Vol. 46 ›› Issue (4): 75-77.

降序且保序有限部分变换半群的幂等元秩

赵平¹, 游泰杰², 徐波²，胡华碧¹

1.贵阳医学院基础医学院, 贵州贵阳 550004; 2.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:2010-04-26 发布日期:2011-04-21
作者简介:赵平(1973- ), 男, 硕士研究生, 副教授, 研究方向为半群理论及编码理论. Email: zhaoping731108@hotmail.com
基金资助:
贵州省科学技术基金资助项目(黔科合J字(2007)2008);黔科合［2010］3174

Idempotent rank in decreasing and order-preserving finite partial transformation semigroups

ZHAO Ping¹, YOU Tai-jie², XU Bo²， HU Hua-bi¹

1. School of Basic Medicine, Guiyang Medical College, Guiyang 550004, Guizhou, China;
2. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, Guizhou, China

Received:2010-04-26 Published:2011-04-21

摘要/Abstract

摘要：

设PC_n是［n］上的降序且保序有限部分变换半群。对n≥3, 证明了半群PC_n是由秩为n-1的幂等元生成的, 且它的秩和幂等元秩都是2n-1。

关键词: 变换半群; 降序; 保序; 幂等元秩; 秩

Abstract:

Let PC_n be the semigroup of all decreasing and order-preserving partial transformations on ［n］. For n≥3, we shall show that the semigroup PC_n is generated by idempotents of rank n-1, and that its rank and idempotent rank are both equal to 2n-1.

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

赵平1, 游泰杰2, 徐波2，胡华碧1. 降序且保序有限部分变换半群的幂等元秩[J]. J4, 2011, 46(4): 75-77.

ZHAO Ping1, YOU Tai-jie2, XU Bo2， HU Hua-bi1. Idempotent rank in decreasing and order-preserving finite partial transformation semigroups[J]. J4, 2011, 46(4): 75-77.

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