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Fuzzy primary ideals: Some ring-theoretic analogues. (English) Zbl 0802.16002

This paper is a natural continuation of the author’s earlier joint work with Dixit and Ajmal on the straightforward fuzzification process of classical ring theory. A characterization of a fuzzy primary ideal as defined by D. Malik and J. Mordeson [Inf. Sci. 53, 237-250 (1991; Zbl 0712.16001)] is given. Furthermore it is proved that every natural power of a fuzzy maximal ideal of a ring constitutes a fuzzy primary ideal. The main result of this paper reveals the algebraic nature of fuzzy primary ideals under a homomorphism; it is shown that there exists a one-to-one correspondence between the set of all \(f\)-invariant primary ideals of a ring \(R\) and the set of all fuzzy primary ideals of a ring \(R'\) being homomorphic to \(R\).
Reviewer: E.Kerre (Gent)

MSC:

16D25 Ideals in associative algebras

Citations:

Zbl 0712.16001
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