r-Regular Near-Rings
Journal Title: International Journal of engineering Research and Applications - Year 2018, Vol 8, Issue 8
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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