A radical for right near-rings: The right Jacobson radical of type-0

Abstract

The notions of a right quasiregular element and right modular right ideal in a near-ring are initiated. Based on these J0r(R), the right Jacobson radical of type-0 of a near-ring R is introduced. It is obtained that J0r is a radical map and N(R)⊆J0r(R), where N(R) is the nil radical of a near-ring R. Some characterizations of J0r(R) are given and its relation with some of the radicals is also discussed.