Paper ID:4597

P-Properties in  Near-Rings

Akın Osman Atagün1, Hüseyin Kamacı1, İsmail Taştekin1& Aslıhan Sezgin2

1Bozok University, Department of Mathematics, 66100 Yozgat, Turkey
2Amasya 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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