P-properties in Near-rings

Abstract

In this paper, assuming that N is a near-ring and P is an ideal of N , the P -center of N , the P -center of an element in N, the P -identities of  N are defined. Their properties and relations are investigated. It is shown that the set of all P -identities in N is a multiplicative subsemigroup of N . Also, P -right and P -left permutable and P -medial near-rings are defined and some properties and connections are given. P -regular and P -strongly regular near-rings are studied. P -completely prime ideals are introduced and some characterizations of -completely prime near-rings are provided. Also, some properties of P -idempotents, P -centers, P -identities in P -completely prime near-rings are investigated. The results that were obtained in this study are illustrated with many examples.