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C-Prime Fuzzy Ideals of Nearrings

In this paper, we introduce the notion of c-prime fuzzy ideal of a near- ring. The cardinality of the image of a c-prime fuzzy ideal can be greater than 2. This is unlike fuzzy prime ideals of rings and that of nearrings. If f : N→ M is an onto nearring homomorphism, we show that the map µ7→ f(µ) defines a one-to-one correspondence between the set of all f-invariant c-prime fuzzy ideals of N and the set of all c-prime fuzzy ideals of M. Finally, we obtain the relationships between c-prime fuzzy ideals and already defined equiprime fuzzy ideals and 3-prime fuzzy ideals of nearrings. 1. Introduction and Preliminaries The definition of fuzzy prime ideal of a ring as well as that of a nearring resulted in stringent conditions namely: (i) the cardinality of the image of a fuzzy prime ideal µ is 2; and (ii) µ(0) = 1. As an attempt to resolve this problem, the present authors in (3) introduced the notions of equiprime fuzzy ideal and 3- prime fuzzy ideal of nearrings and also studied the radical properties based on these ideals. In this paper, we introduce the notion of c-prime fuzzy ideal of a nearring and study the interconnection with the above notions. We review some definitions and results for the sake of completeness. Throughout the paper, N and M will denote right nearrings. A standard refer- ence on nearrings is Pilz (13) and on rings is Anderson and Fuller (2). ((6)) An ideal I of N is called c-prime if a, b ∈ N and ab ∈ I implies a ∈ I or b ∈ I. N is called c-prime nearring if {0} is a c-prime ideal of N.