The traditional approach to Jacobson radicals for (right) near-rings has always been via left representations, i.e. using left \(N\)-groups. For rings this left-right distinction is not important since both lead to the same radical, but for near-rings this is not the case. Only during the last number of years, Jacobson type radicals for near-rings using right representations have been defined and are being investigated.
This paper is in this vein – the authors define a Jacobson type radical for near-rings using a right representation. From a radical theoretic viewpoint the results are interesting and rewarding: a Kurosh-Amitsur radical with highly desirable properties is obtained. The contribution of these new notions to the structure theory of near-rings has not yet been addressed.