P-properties in Near-rings

Akın Osman Atagün (Department of Mathematics, Ahi Evran University, Kırşehir 40100)
Hüseyin Kamacı (Department of Mathematics, Yozgat Bozok University, Yozgat 66100)
Ä°smail TaÅŸtekin (Department of Mathematics, Yozgat Bozok University, Yozgat 66100, Turkey)
Aslıhan Sezgin (Department of Elementary Education, Amasya University, Amasya 05100)

Journal of Mathematical and Fundamental Sciences
Vol. 51 No. 2 (2019)

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.