ON WEAKLY 2-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS

Badawi A., TEKİR Ü., Yetkin E.

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, vol.52, no.1, pp.97-111, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 1
  • Publication Date: 2015
  • Doi Number: 10.4134/jkms.2015.52.1.097
  • Journal Name: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.97-111
  • Keywords: primary ideal, weakly primary ideal, prime ideal, weakly prime ideal, 2-absorbing ideal, n-absorbing ideal, weakly 2-absorbing ideal, 2-absorbing primary ideal, weakly 2-absorbing primary 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 weakly 2-absorbing primary ideal which is a generalization of weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever a, b,c is an element of R and 0 not equal 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 weakly 2-absorbing primary ideals and examples of weakly 2-absorbing primary ideals are given.