• EIFP Near-fields an extension of Near-rings and regular -near-rings (EIFP-NF-E-NR-R--NR)

Abstract

A near-field N is defined  to be EI F P  if ab = 0 implies aE(N)b ⊆J (N) for a, bÎN where E(N) and  J (N) stand respectively for the set of idempotents, Levitzki radical and the Jacobson radical of N. Some properties and characterizations are given. And it follows that for an EIFP near-field N, we proved that (1) N is an commutative near-field if and only if N is a strongly left idempotent reflexive near-field; (2) N is a strongly  regular  near-field if and only if N  is a von Neu- mann  regular  near-field; (3)  N  is a clean  near-field if and only if N is an exchange near-filed;(4)Nis a (S, 2)-near-field if and only if Z/2Z is not a homomorphic  image of N.