A Kurosh-Amitsur Completely Prime Radical for Near-rings

Authors

  • Kilaru J. Lakshminarayana Koneru Lakshmaiah Education Foundation
  • V.B.V.N. Prasad Koneru Lakshmaiah Education Foundation
  • Srinivasa Rao Ravi University College of Sciences, Acharya Nagarjuna University
  • Siva Prasad Korrapati University College of Sciences, Acharya Nagarjuna University
  • V Ramakrishna Amathi Department of Mathematics, R.V.R and J.C College of Engineering,Chowdavaram, Guntur-522019, Andhra Pradesh, India https://orcid.org/0000-0001-6247-8454

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6576

Keywords:

near-ring, $N$-group, prime$N$-groups of type~$r(1)$, K-A radical

Abstract

Two generalizations of the completely prime radical of rings to near-rings, namely the completely prime radical of near-rings and the completely equiprime radical of near-rings were introduced and studied. First one is not a Kurosh-Amitsur radical but the second one is a special radical in near-rings. In this article another generalization of the   completely prime radical of rings  is introduced in near-rings using right modules of near-rings. For this  completely prime right $N$-groups of type-$r(1)$ are introduced in near-rings, $N$ is a near-ring. Making use of these right $N$-groups of type-$r(1)$, the completely prime radical of near-rings of type-$r(1)$ is introduced. It is observed that the completely prime radical  of\\ type-r(1) is a Kurosh-Amitsur radical.

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Algebra

License

Copyright (c) 2025 Kilaru J. Lakshminarayana, V.B.V.N. Prasad, Srinivasa Rao Ravi, Siva Prasad Korrapati, V Ramakrishna Amathi

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How to Cite

A Kurosh-Amitsur Completely Prime Radical for Near-rings. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6576. https://doi.org/10.29020/nybg.ejpam.v18i3.6576