• 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.
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