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\((\lambda,\mu)\)-fuzzy prime ideals and \((\lambda,\mu)\)-fuzzy primary ideals in semigroups. (English) Zbl 1332.20108

Summary: In order to generalize the notions of various fuzzy ideals in a semigroup, the concepts of \((\lambda,\mu)\)-fuzzy prime ideal and \((\lambda,\mu)\)-fuzzy primary ideal are introduced based on \((\lambda,\mu)\) cut set. Some properties of \((\lambda,\mu)\)-fuzzy prime ideal are discussed and several equivalent conditions are obtained.

MSC:

20N25 Fuzzy groups
20M12 Ideal theory for semigroups
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