Kurosh-Amitsur Right Jacobson Radical of Type 0 for Right Near-Rings

Abstract

By a near-ring we mean a right near-ring. J0r, the right Jacobson radical of type 0, was introduced for near-rings by the first and second authors. In this paper properties of the radical J0r are studied. It is shown that J0r is a Kurosh-Amitsur radical (KA-radical) in the variety of all near-rings R, in which the constant part Rc of R is an ideal of R. So unlike the left Jacobson radicals of types 0 and 1 of near-rings, J0r is a KA-radical in the class of all zero-symmetric near-rings. J0r is not s-hereditary and hence not an ideal-hereditary radical in the class of all zero-symmetric near-rings.