Special Right Jacobson Radicals for Right Near-rings

Abstract

In this paper three more right Jacobson-type radicals, J r g , are introduced for near-rings which generalize the Jacobson radical of rings, 2 f0;1;2g. It is proved that J r g is a special radical in the class of all near-rings. Unlike the known right Jacobson semisimple near-rings, a J r g -semisimple near-ring R with DCC on right ideals is a direct sum of minimal right ideals which are right R-groups of type-g , 2 f0;1;2g. Moreover, a nite right g2-primitive near-ring R with eRe a non-ring is a near-ring of matrices over a near-eld (which is isomorphic to eRe), where e is a right g2-primitive idempotent in R.