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Fuzzy subrings and ideals redefined. (English) Zbl 0878.16025

Summary: \((\varepsilon, \varepsilon\vee q)\)-fuzzy subrings and ideals of a ring are defined. The concepts of \((\varepsilon, \varepsilon\vee q)\)-fuzzy semiprime, prime, semiprimary, primary and maximal ideals are introduced and characterization of such fuzzy ideals are obtained. \((\varepsilon, \varepsilon\vee q)\)-fuzzy cosets determined by \((\varepsilon, \varepsilon\vee q)\)-fuzzy ideals and \((\varepsilon, \varepsilon\vee q)\)-fuzzy radicals of \((\varepsilon, \varepsilon\vee q)\)-fuzzy ideals are discussed.

MSC:

16Y99 Generalizations
16D25 Ideals in associative algebras
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References:

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