A generalization of 2-primal near-rings

Abstract

In this note we generalize the notion of 2-primal and nil-primal nearrings. For a Hoehnke radical ρ we introduce the notion of ρ–primal near-rings. 2-primal and nil-primal near-rings are examples of ρ–primal near-rings. We show that many of the results for 2-primal and nil-primal rings and near-rings can be proved for ρ–primal near-rings.