# P-properties in Near-rings

## DOI:

https://doi.org/10.5614/j.math.fund.sci.2019.51.2.5## Keywords:

near-ring, P-center, P-completely prime ideal, P-regular, P-strongly regular## 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.

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