### P-Properties in Near-Rings

**Akın Osman Atagün ^{1}, Hüseyin Kamacı^{1}, İsmail Taştekin^{1}& Aslıhan Sezgin^{2}**

^{1}Bozok University, Department of Mathematics, 66100 Yozgat, Turkey

^{2}Amasya University, Department of Elementary Education, 05100 Amasya, Turkey

Received April 25th, 2017, 1st Revision September 21st, 2018, 2nd Revision October 19, 2018, Accept to Publish December 26th, 2018.

**Abstract.** We define P-center of N, P-center of an element in N, P-identities of N and investigate these properties and relations, when N is a near-ring and P is an ideal of N. We show that the set of all P-identities in N is a multiplicative subsemigroup of N. We also define P-right (P-left) permutable and P-medial near-rings and give some properties and connections. We study P-regular and P-strongly regular near-rings. We introduce P-completely prime ideals and provide some characterizations of P-completely prime near-rings. We also investigate some properties of P-idempotents, P-centers, P-identities in P-completely prime near-rings. We illustrate the results, which are obtained in this paper, with many examples.

**Keywords :** Near-ring, P-completely prime ideal, P-center, P-regular, P-strongly regular.

Mathematics Subject Classification 2010: 16Y30,16N60

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