Published online by Cambridge University Press: 09 April 2009
It is known that in a near-ring N the Levitzki radical L(N), that is, the sum of all locally nilpotent ideals, is the intersection of all the prime ideals P in N such that N/P has zero Levitzki radical. The purpose of this 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-semi-prime ideal and show that P is an l-semi-prime ideal if and only if N/P has zero Levitzki radical. We get another characterization of the Levitzki radical of the near-ring as the intersection of all the l-semi-prime ideals.