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Fuzzy prime ideals of pseudo-MV algebras. (English) Zbl 1132.06006

Pseudo-MV algebras, as a non-commutative generalization of MV-algebras, are an algebraic counterpart of the non-commutative Łukasiewicz infinite-valued propositional logic. The paper deals with fuzzy ideals of pseudo-MV algebras. The author gives a new construction of the fuzzy ideal generated by a fuzzy set of a pseudo-MV algebra. Further, fuzzy prime ideals are introduced and connections between them and prime ideals of pseudo-MV algebras are described.

MSC:

06D35 MV-algebras
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