Fuzzy Quasi-Ideals of Ordered Semigroups

Abstract. In this paper, we characterize ordered semigroups in terms of fuzzy quasi-ideals. We characterize left simple, right simple and completely regular ordered semigroups in terms of fuzzy quasi-ideals. We define semiprime fuzzy quasi-ideal of ordered semigroups and characterize completely regular ordered semigroup in terms of semiprime fuzzy quasi-ideals. We also study the decomposition of left and right simple ordered semigroups having the property a ≤ a 2 for all a ∈ S, by means of fuzzy quasi-ideals. Mathematics Subject Classification: 06F05, 06D72, 08A72 Keywords and phrases: Subsemigroups, left (right) ideals, quasi-(bi-) ideals, left (right) regular, left (right) simple ordered semigroups, completely regular ordered semigroups, fuzzy sets, fuzzy subsemigroup, fuzzy left (right) ideals, fuzzy quasi-(bi-) ideals, semiprime (resp. semiprime fuzzy) ideals of ordered semigroups

Fuzzy Quasi-ideals of Ordered Semigroups

In this paper, we characterize ordered semigroups in terms of fuzzy quasi-ideals. We characterize left simple, right simple and completely regular ordered semigroups in terms of fuzzy quasi-ideals. We define semiprime fuzzy quasi-ideal of ordered semigroups and characterize completely regular ordered semigroup in terms of semiprime fuzzy quasi-ideals. We also study the decomposition of left and right simple ordered semigroups having the property a a 2 for all a 2 S, by means of fuzzy quasi-ideals