FUZZY IMPLICATIVE AND BOOLEAN IDEALS OF MV-ALGEBRAS

We show how to obtain results in MV-algebras by considering their fuzzy ideals. In particular we prove the following theorem: Let mu be a fuzzy ideal of an MV-algebra X. Then the following are equivalent: (1)mu(x boolean AND (x) over bar) = mu(0) for all x is an element of X, (2)mu(x(n)) = mu(x) for all x is an element of X and all n greater than or equal to 1, (3) X/X(mu), is a Boolean algebra, (4) mu is fuzzy implicative. If I is an ideal of X and we take mu = chi(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.