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.