Kurosh–Amitsur Right Jacobson Radicals of Type-1 and 2 for Right Near-Rings

Abstract

Near-rings considered are right near-rings. Let ν ∈ {1, 2}. J r ν , the right Jacobson radical of type-ν, was introduced for near-rings by the first and second authors. In this paper properties of these radicals J r ν are studied. It is shown that J r ν is a Kurosh-Amitsur radical (KA-radical) in the variety of all near-rings R in which the constant part R c of R is an ideal of R. Thus, unlike the left Jacobson radical of type-1 of near-rings, J r 1 is a KA-radical in the class of all zero-symmetric near-rings. J r ν is not s-hereditary and hence not an ideal-hereditary radical in the class of all zero-symmetric near-rings.