P-properties in Near-rings

Akın Osman Atagün, Hüseyin Kamacı, İsmail Taştekin, Aslıhan Sezgin

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.

Keywords


near-ring; P-center; P-completely prime ideal; P-regular; P-strongly regular

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DOI: http://dx.doi.org/10.5614%2Fj.math.fund.sci.2019.51.2.5

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