Abstract
In this paper, we present the notions of equiprime fuzzy ideal, 3-prime fuzzy ideal and c-prime fuzzy ideal of a nearring. We characterize these fuzzy ideals using level subsets and fuzzy points. If f: N → M is an onto nearring homomorphism, we show that the map \({\mu}\, {\mapsto}\, f(\mu)\) defines a one-to-one correspondence between the set of all f-invariant (alternatively with sup property) equiprime (3-prime and c-prime, respectively) fuzzy ideals of N and the set of all equiprime (3-prime and c-prime, respectively) fuzzy ideals of M. Finally, we define fuzzy cosets determined by generalized fuzzy ideals; obtain fundamental results and isomorphism theorems.
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Acknowledgments
The authors thank Prof. Stefan Veldsman, Sultan Qaboos University, Sultanate of Oman, for his comments and suggestions. The authors also thank the anonymous referees for their constructive comments. The first and the second author acknowledge Manipal University and the third author acknowledges Acharya Nagarjuna University for their encouragement.
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Kedukodi, B.S., Kuncham, S.P. & Bhavanari, S. Equiprime, 3-prime and c-prime fuzzy ideals of nearrings. Soft Comput 13, 933–944 (2009). https://doi.org/10.1007/s00500-008-0369-x
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DOI: https://doi.org/10.1007/s00500-008-0369-x