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\(\sigma\)-fuzzy ideals of distributive \(p\)-algebras. (English) Zbl 1438.06039

Summary: In this paper, we introduce the concept of \(\sigma\)-fuzzy ideals in distributive \(p\)-algebras. It is proved that the set of all \(\sigma\)-fuzzy ideals forms a complete distributive lattice. Moreover, the class of all \(\sigma\)-fuzzy ideals of a distributive \(p\)-algebra is isomorphic to the class of fuzzy ideals of the lattice of all booster ideals. Finally, we prove that the image and pre-image of \(\sigma\)-fuzzy ideals are also \(\sigma\)-fuzzy ideals.

MSC:

06D72 Fuzzy lattices (soft algebras) and related topics
06B10 Lattice ideals, congruence relations
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