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L-fuzzy congruences and L-fuzzy kernel ideals in Ockham algebras. (English) Zbl 1477.06039

Summary: In this paper, we study fuzzy congruence relations and kernel fuzzy ideals of an Ockham algebra \((A, f)\), whose truth values are in a complete lattice satisfying the infinite meet distributive law. Some equivalent conditions are derived for a fuzzy ideal of an Ockham algebra \(A\) to become a fuzzy kernel ideal. We also obtain the smallest (respectively, the largest) fuzzy congruence on \(A\) having a given fuzzy ideal as its kernel.

MSC:

06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects)
06B10 Lattice ideals, congruence relations
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