n-Ideals of Commutative Rings

TEKİR Ü., KOÇ S., Oral K. H.

FILOMAT, vol.31, no.10, pp.2933-2941, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 10
  • Publication Date: 2017
  • Doi Number: 10.2298/fil1710933t
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2933-2941
  • Keywords: prime ideal, r-ideal, n-ideal, 2-ABSORBING PRIMARY IDEALS, PRIME IDEALS
  • Marmara University Affiliated: Yes

Abstract

In this paper, we present a new classes of ideals: called n-ideal. Let R be a commutative ring with nonzero identity. We define a proper ideal I of R as an n-ideal if whenever ab is an element of I with a is not an element of root 0, then b is an element of I for every a, b is an element of R. We investigate some properties of n-ideals analogous with prime ideals. Also, we give many examples with regard to n-ideals.