Different prime N-ideals and IFP N-Ideals

Taşdemir F., Atagun A. O., Altındiş H.

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, vol.44, no.4, pp.527-542, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 4
  • Publication Date: 2013
  • Doi Number: 10.1007/s13226-013-0028-5
  • Journal Name: INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.527-542
  • Keywords: Prime near-ring, prime ideal, prime N-group, 3-prime N-ideal, completely prime N-ideal, IFP N-ideal
  • Yozgat Bozok University Affiliated: Yes

Abstract

We provide some characterizations of completely prime (completely semiprime) and 3-prime (3-semiprime) N-groups. The relationship between a 3-prime (completely prime) N-ideal P of an N-group I" and the ideal (P: I") of the near-ring N is investigated. Moreover, the notion of IFP N-ideal is defined. We prove that the concept of IFP N-ideal occurs naturally where N is a left permutable (left self distributive, subcommutative) near-ring and I" a monogenic N-group. Also, we obtain some relationships between an IFP N-ideal P of an N-group I" and the ideal (P: I") of the near-ring N.