严格π-正则半群上的fuzzy同余  

Fuzzy Congruences on Strictly π-Regular Semigroups

作　　者：李春华[1,2] 刘二根[1] 

机构地区：[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

出　　处：《中山大学学报（自然科学版）》2011年第5期11-14,共4页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(11061014);江西省自然科学基金资助项目(2007GZS0715);江西省教育厅科研基金资助项目(GJJ10453);华东交通大学科研基金资助项目(01305131)

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。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.

关 键 词：严格π-正则半群 fuzzy同余 fuzzy群同余 

分 类 号：O152.7[理学—数学]