Completely Equiprime Ideals of Near-Ring Modules

Abstract

In this study, the concept of completely equiprime N-ideal (ideal of near-ring modules) is introduced. Also the interconnections of completely equiprime, equiprime and completely prime N-ideals are considered. It is proved that if  P is a completely equiprime ideal of an N-group (near-ring module) Γ , then (P: Γ ) is a completely equiprime ideal of a near-ring N. The converse relation does not hold in general, however we provide some additional conditions for the converse to be true. The connection between the concepts of completely equiprime N-ideal and IFP N-ideal is also observed.