r-Regular Near-Rings

Abstract

In this paper the terms, regular near-rings,r- regular near-rings, symmetric near-ring, weakly regular near-ring, completely prime ideal, 1-prime ideal, 1-semiprime ideals are introduced. We investigated some basic properties for r- regular near-rings. We use completely prime ideal, maximal ideal, 1-prime ideal, 1-semiprime ideals to characterize r- regular near-rings. Finally, we proved that the following conditions concerning for r-regular nearring with identity and has IFP are equivalent (1) N is regular near-ring. (2) 𝐴 = 𝐴for every N-subgroup A of N. (3) N is left bipotent. (4) N is strongly regular near-ring. And also it is proved that the following conditions concerning for a near-ring 𝑁 ∈ 𝜂0with identity are equivalent (1) N is r - regular and has IFP and (2) N is reduced and every completely prime ideal is maximal.

Authors and Affiliations

Marisetti Sowjanya, A. Gangadhara Rao, A. Anjaneyulu, Radha rani Tammileti

Keywords

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  • EP ID EP395039
  • DOI 10.9790/9622-0808021119.
  • Views 138
  • Downloads 0

How To Cite

Marisetti Sowjanya, A. Gangadhara Rao, A. Anjaneyulu, Radha rani Tammileti (2018). r-Regular Near-Rings. International Journal of engineering Research and Applications, 8(8), 11-19. https://europub.co.uk/articles/-A-395039