P-properties in Near-rings


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Atagun A. O. , KAMACI H. , Tastekin I., SEZGİN SEZER A.

JOURNAL OF MATHEMATICAL AND FUNDAMENTAL SCIENCES, vol.51, no.2, pp.152-167, 2019 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.5614/j.math.fund.sci.2019.51.2.5
  • Title of Journal : JOURNAL OF MATHEMATICAL AND FUNDAMENTAL SCIENCES
  • Page Numbers: pp.152-167

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 P-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.