中山大学学报自然科学版 ›› 2011, Vol. 50 ›› Issue (5): 11-14.

• 研究论文 • 上一篇    下一篇

严格π-正则半群上的fuzzy同余

李春华1,2, 刘二根1   

  1. ( 1. 华东交通大学基础科学学院,江西 南昌 330013;2. 华南师范大学数学科学学院, 广东 广州 510631)
  • 收稿日期:2010-10-19 修回日期:1900-01-01 出版日期:2011-09-25 发布日期:2011-09-25

Fuzzy Congruences on Strictly πRegular Semigroups

LI Chunhua1,2, LIU Ergen1   

  1. (1.School of Basic Science, East China Jiaotong University, Nanchang 330013, China;2. School of Mathematics, South China Normal University, Guangzhou 510631, China)
  • Received:2010-10-19 Revised:1900-01-01 Online:2011-09-25 Published:2011-09-25

摘要: π-正则半群S称为严格π-正则的,如果其正则元集为S的理想且为S的完全正则子半群。这里利用半群fuzzy同余的概念,研究了π-正则半群上fuzzy同余的性质。在此基础上, 给出了严格π-正则半群上fuzzy同余的性质和特征, 并给出了严格π-正则半群上群同余的刻画,得到了严格π-正则半群上fuzzy同余为fuzzy群同余的充要条件。

关键词: 严格π-正则半群, fuzzy同余, fuzzy群同余

Abstract: A πregular semigroup S is called strictly πregular, if the set of regular elements of S is an ideal of S and is a completely regular subsemigroup of S. We use the notion of a fuzzy congruence relation on semigroups to study some properties of fuzzy congruences on πregular semigroups. Some properties and characterizations of fuzzy congruences on strictly πregular semigroups are given, and the group congruence on such semigroups is obtained. Finally, sufficient and necessary conditions for a fuzzy congruence on a strictly πregular semigroup to be a fuzzy group congruence are proved.

Key words: strictly πregular semigroup, fuzzy congruence, fuzzy group congruence

中图分类号: