• A NOTE ON THE LEVITZKI RADICAL OF A NEAR FIELDS (LR - NF)

Abstract

In this paper we study and obtain some results on Levitzki radical of a near-field over a defined near-ring earlier. It is known that a near-field N the Levitzki radical L(N) i.e., the sum of all locally nilpotent ideals is the intersection of all the prime ideals P in  near-field N such that N / P has zero Levitzki radical. The purpose of these note is to prove that L(N) is the intersection of a certain class of prime ideals called l-prime ideals. Every l-prime ideal P is such that N / P has zero Levitzki radical. We also introduce an l-prime ideal if and only if N / P has zero Levitzki radical of the near-field as the intersection all the l-semi-prime ideals.