Kumar, Rajesh Fuzzy primary ideals: Some ring-theoretic analogues. (English) Zbl 0802.16002 Bull. Calcutta Math. Soc. 84, No. 4, 301-308 (1992). 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) Cited in 1 Document MSC: 16D25 Ideals in associative algebras Keywords:fuzzification; fuzzy maximal ideal; fuzzy primary ideals; homomorphism; \(f\)-invariant primary ideals Citations:Zbl 0712.16001 PDFBibTeX XMLCite \textit{R. Kumar}, Bull. Calcutta Math. Soc. 84, No. 4, 301--308 (1992; Zbl 0802.16002)