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].