关于循环系的(P)-覆盖的一个推广

J4 ›› 2012, Vol. 47 ›› Issue (4): 94-96.

关于循环系的(P)-覆盖的一个推广

赵梅梅,乔虎生*

西北师范大学数学与信息科学学院, 甘肃兰州 730070

收稿日期:2011-02-18 出版日期:2012-04-20 发布日期:2012-06-28
通讯作者: 乔虎生(1974- ), 男, 教授, 主要研究方向为半群理论. Email: qiaohs@nwnu.edu.cn
作者简介:赵梅梅 (1986- ), 女, 硕士研究生，主要研究方向为半群理论. Email: zhaomeimei125@163.com
基金资助:
国家自然科学基金资助项目(10901129); 高等学校博士学科点专项科研基金(20096203120001)

On a generalization of (P)-covers of cyclic acts

ZHAO Mei-mei, QIAO Hu-sheng*

College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, Gansu, China

Received:2011-02-18 Online:2012-04-20 Published:2012-06-28

摘要/Abstract

摘要：

设S是幺半群, I是S的一个理想。利用理想I定义了条件(PI)。给出了循环系满足条件(PI)的充分必要条件, 并研究了所有循环系具有(PI)-覆盖的幺半群。若理想I取成S, 则条件(PI)和条件(P)等价, 推广了已有的结果。

关键词: 循环S-系; 条件(P); 覆盖

Abstract:

Let S be a monoid and I an ideal of S. Using the ideal I the condition (PI) is defined. The necessary and sufficient condition of cyclic act satisfying condition (PI) is given and the monoids over which every cyclic act has a (PI)-cover are investigated. If the ideal I equals to S, the condition (PI) and condition (P) are equivalent, so the main results in the reference are generalized.

Key words: cyclic S-act; condition (P); cover

赵梅梅,乔虎生*. 关于循环系的(P)-覆盖的一个推广[J]. J4, 2012, 47(4): 94-96.

ZHAO Mei-mei, QIAO Hu-sheng*. On a generalization of (P)-covers of cyclic acts[J]. J4, 2012, 47(4): 94-96.

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