Special Right Jacobson Radicals for Right Near-rings

- Journal title : Kyungpook mathematical journal
- Volume 54, Issue 4, 2014, pp.595-606
- Publisher : Department of Mathematics, Kyungpook National University
- DOI : 10.5666/KMJ.2014.54.4.595

Title & Authors

Special Right Jacobson Radicals for Right Near-rings

Rao, Ravi Srinivasa; Prasad, Korrapati Siva;

Rao, Ravi Srinivasa; Prasad, Korrapati Siva;

Abstract

In this paper three more right Jacobson-type radicals, , are introduced for near-rings which generalize the Jacobson radical of rings, . It is proved that is a special radical in the class of all near-rings. Unlike the known right Jacobson semisimple near-rings, a -semisimple near-ring R with DCC on right ideals is a direct sum of minimal right ideals which are right R-groups of type-, . Moreover, a finite right -primitive near-ring R with eRe a non-ring is a near-ring of matrices over a near-field (which is isomorphic to eRe), where e is a right -primitive idempotent in R.

Keywords

Language

English

Cited by

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