严格π-正则半群上的fuzzy同余

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 5 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.