Generalizations of 2-absorbing primaryideals of commutative rings

Abstract

Let R be a commutative ring with 1 = 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 φ -2-absorbing primary ideals. Let φ : S(R) → S(R) ∪ ∅ be a function. A proper ideal I of R is said to be a φ -2-absorbing primary ideal of R if whenever a, b, c ∈ R with abc ∈ I −φ(I) implies ab ∈ I or ac ∈ √ I or bc ∈ √ I . A number of results concerning φ -2-absorbing primary ideals are given.