No abstract

In this paper three more right Jacobson-type radicals, J r gν , are introduced for near-rings which generalize the Jacobson radical of rings, ν ∈ {0, 1, 2}. It is proved that J r gν is a special radical in the class of all near-rings. Unlike the known right Jacobson semisimple near-rings, a J r gν-semisimple near-ring R with DCC on right ideals is a direct sum of minimal right ideals which are right R-groups of type-gν , ν ∈ {0, 1, 2}. Moreover, a finite right g2-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 g2-primitive idempotent in R.

No abstract

No abstract