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A KUROSH-AMITSUR LEFT JACOBSON RADICAL FOR RIGHT NEAR-RINGS

  • Rao, Ravi Srinivasa (DEPARTMENT OF MATHEMATICS P.G. CENTRE P.B. SIDDHARTHA COLLEGE OF ARTS AND SCIENCE) ;
  • Prasad, K.Siva (DEPARTMENT OF MATHEMATICS CHALAPATHI INSTITUTE OF ENGINEERIGN AND TECHNOLOGY)
  • Published : 2008.08.31

Abstract

Let R be a right near-ring. An R-group of type-5/2 which is a natural generalization of an irreducible (ring) module is introduced in near-rings. An R-group of type-5/2 is an R-group of type-2 and an R-group of type-3 is an R-group of type-5/2. Using it $J_{5/2}$, the Jacobson radical of type-5/2, is introduced in near-rings and it is observed that $J_2(R){\subseteq}J_{5/2}(R){\subseteq}J_3(R)$. It is shown that $J_{5/2}$ is an ideal-hereditary Kurosh-Amitsur radical (KA-radical) in the class of all zero-symmetric near-rings. But $J_{5/2}$ is not a KA-radical in the class of all near-rings. By introducing an R-group of type-(5/2)(0) it is shown that $J_{(5/2)(0)}$, the corresponding Jacobson radical of type-(5/2)(0), is a KA-radical in the class of all near-rings which extends the radical $J_{5/2}$ of zero-symmetric near-rings to the class of all near-rings.

References

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