Equiprime n-ideals of monogenic n-groups

Abstract

In this paper we introduce the notion of equiprime iV-ideals where N is a near-ring. We consider the interconnections of equiprime, 3-prime and completely prime N-ideals of a monogenic N-group $Gamma$. We show that if P is an equiprime iV-ideal of $Gamma$, then $(P :Gamma)_N$ is an equiprime ideal of N, and that the converse holds when N is a right permutable near-ring and $Gamma$ is a monogenic N-group.