Abstract
Abstract We show how to obtain results in MV -algebras by considering their fuzzy ideals. In particular we prove the following theorem: Let μ be a fuzzy ideal of an MV -algebra X . Then the folllowing are equivalent: (1) μ (x ∧ x = μ(0) for all x ϵ X , (2) μ ( x n ) = μ ( x ) for all x ϵ X and all n ⩾ 1, (3) X / X μ is a Boolean algebra, (4) μ is fuzzy implicative. If I is an ideal of X and we take μ = χ I then we obtain corresponding results for the ideal I and X . We show how to extend fuzzy prime and fuzzy implicative ideals. Various fuzzy radicals are considered and related to the corresponding radicals of the algebra, and we show how they live in the spectrum of the algebra.
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