关于左半完备富足半群的Fuzzy同余注记  

A Note on Fuzzy Congruences on Left Semi-Perfect Abundant Semigroups

作　　者：李春华[1] 刘二根[1] 徐保根[1] 

机构地区：[1]华东交通大学基础科学学院,江西南昌330013

出　　处：《四川师范大学学报（自然科学版）》2012年第6期755-758,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11261018;11061014);江西省自然科学基金(20122BAB201018);江西省教育厅科研基金(10GJJ453)资助项目

摘　　要：半群S称为富足的,若它的所有L*类及R*类都含幂等元.富足半群S称为左半完备的,若它的幂等元集为左拟正规带.利用富足半群上Fuzzy好同余和Fuzzy消去同余的概念,给出了左半完备富足半群上Fuzzy好同余和Fuzzy消去同余的性质,得到了此类半群的刻画,并证明了富足半群为左半完备富足半群的充要条件.以上结论是对El-Qallali和Fountain关于拟适当半群研究结果的推广和补充.A semigroup S is called abundant if every L＊ class and every R＊ class of S contains an idempotent.An abundant semigroup is called left semi-perfect if its set of idempotents forms a left quasi-normal band.Using the concepts of a fuzzy good congruence relation and a fuzzy cancellative congruence relation on abundant semigroups,some properties and characterizations of fuzzy good congruences and fuzzy cancellative congruences on left semi-perfect abundant semigroups are given.Finally,sufficient and necessary conditions for an abundant semigroup to be left semi-perfect are proved.These results generalize and strengthen the results of El-Qallali and Fountain on quasi-adequate semigroups.

关 键 词：富足半群 左半完备 左拟正规带 Fuzzy好同余 

分 类 号：O152.7[理学—数学]