Abstract
The notions of fuzzy ideal and fuzzy prime ideal of a ring with truth values in a complete lattice satisfying the infinite meet distributive law are introduced which generalize the existing notions with truth values in the unit interval of real numbers. A procedure to construct any fuzzy ideal from a family of ideals with certain conditions is established. All fuzzy prime (maximal) ideals of a given ring are determined by establishing a one-to-one correspondence between fuzzy prime (maximal) ideals and the pairs ( P, α), where P is a prime (maximal) ideal of the ring and α is a prime element (dual atom) in the complete lattice.
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