Abstract
In this chapter, we characterize prime fuzzy ideals of a semigroup S. Sections 7.1–7.11 are essentially from [151]. We show that a nonconstant fuzzy ideal f of a semigroup S is prime if and only if f is two-valued and there exists an element x0 in S such that f(x0) = 1 and f1 = {x ∈ S | f(x) = 1} is a prime ideal of S. We also consider the concepts of weakly prime fuzzy ideals, completely prime fuzzy ideals and weakly completely prime fuzzy ideals of a semigroup S. We establish relations among four classes of prime ideals.
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