Left prime weakly regular near-rings

Abstract

In this paper we introduce the notion of left prime weakly regular, left primeweakly $ \pi $-regular and left prime pseudo $ \pi $-regular near-rings. We alsointroduce the concept of strong left prime weakly regular near-rings. We haveobtained conditions for a near-ring $ N $ to be left prime pseudo $ \pi $-regular.We have also obtained conditions for a near-ring $ N $ to be strong left primepseudo $ \pi $-regular. Finally we have answered the open question given in [1].