On prime, quasi-prime, weakly quasi-prime fuzzy left ideals of semigroups (Q5951701)

First the author introduces the concepts of a fuzzy left (right) ideal of a semigroup. Then the concept of a prime fuzzy left ideal is introduced and characterized in terms of fuzzy singletons. It is shown that this prime notion is a natural fuzzification of the crisp notion. Next quasi-prime fuzzy and weakly quasi-prime left ideals are defined and characterized. For commutative semigroups the author shows equivalence of the three notions (prime, quasi-prime and weakly quasi-prime) for a fuzzy left ideal. Finally, based on the notion of idempotency for a fuzzy left ideal of a semigroup, the concept strongly semisimple semigroup is introduced and 5 characterizations of this concept are outlined.