Generalizations of 2-absorbing primary ideals of commutative rings

Badawi A., TEKİR Ü., ASLANKARAYİĞİT UĞURLU E., Ulucak G., Yetkin Celikel E.

TURKISH JOURNAL OF MATHEMATICS, vol.40, no.3, pp.703-717, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 3
  • Publication Date: 2016
  • Doi Number: 10.3906/mat-1505-43
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.703-717
  • 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, phi-prime ideal, phi-2-primary ideal, phi-2-absorbing ideal
  • Marmara University Affiliated: Yes

Abstract

Let R be a commutative ring with 1 not equal 0 and S(R) be the set of all ideals of R. In this paper, we extend the concept of 2-absorbing primary ideals to the context of 0-2-absorbing primary ideals. Let phi : S(R) -> S(R) U null set be a function. A proper ideal I of R is said to be a phi-2-absorbing primary ideal of R if whenever a, b, c is an element of R with abc is an element of I - phi (I) implies ab is an element of I or ac is an element of root I or be E. A number of results concerning phi-2-absorbing primary ideals are given.