ON 2-ABSORBING PRIMARY IDEALS IN COMMUTATIVE RINGS

Badawi A., TEKİR Ü., Yetkin E.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.51, no.4, pp.1163-1173, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 4
  • Publication Date: 2014
  • Doi Number: 10.4134/bkms.2014.51.4.1163
  • Journal Name: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1163-1173
  • Keywords: primary ideal, prime ideal, 2-absorbing ideal, n-absorbing ideal
  • Marmara University Affiliated: Yes

Abstract

Let R be a commutative ring with 1 not equal 0. In this paper, we introduce the concept of 2-absorbing primary ideal which is a generalization of primary ideal. A proper ideal I of R is called a 2-absorbing primary ideal of R if whenever a, b,c is an element of R and abc is an element of I, then ab is an element of I or ac is an element of root I or bc is an element of root I. A number of results concerning 2-absorbing primary ideals and examples of 2-absorbing primary ideals are given.