Satyanarayana, Bhavanari and Kuncham, Syam Prasad and Kumar, Pradeep T and Srinivas, T (2007) Some Results On Fuzzy Cosets and Homomorphisms of N-Groups. East Asian Mathematical Journal, 23 (1). pp. 23-36.

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Abstract

In this paper we consider the fuzzy ideals of N-group G where N is a nearring. We introduce fuzzy ideal θμ of the quotient N-group G/μ with respect to a fuzzy ideal μ of G. If μ is a fuzzy ideal of G and θ a fuzzy ideal of G/μ such that θμ ⊆ θ and θμ(0) = θ(0), then corresponding σθ : G → [0, 1] is defined and proved that it is a fuzzy ideal of G such that μ ⊆ σθ and μ(0) = σθ(0). We also prove some results on homomorphisms and fuzzy ideals of N-groups. The image and preimage of fuzzy ideal μ under N-group homomorphism were studied. Finally it is obtained that if f : G → G1 is an epimorphism of N-groups, then there is an order preserving bijection between the fuzzy ideals of G1 and the fuzzy ideals of G that are constant on kerf. Some examples related to these concepts were illustrated.

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