phi-2-ABSORBING IDEALS
A. Khaksari · International Journal of Pure and Apllied Mathematics · 2015
Let R be a commutative ring with identity.2-absorbing ideals have been studied by A. Badawi.A proper ideal I of R is 2-absorbing if a, b, c ∈ R with abc ∈ I implies ab ∈ I or ac ∈ I or bc ∈ I. Let ϕ : I(R) → I(R) ∪ {∅} be a function where I(R) is the set of ideals of R. We call a proper ideal I of R a ϕ-2-absorbing ideal if a, b, c ∈ R with abc ∈ Iϕ(I) implies ab ∈ I or ac ∈ I or bc ∈ I.So taking ϕ ∅ (J) = ∅ (resp., ϕ 0 (J) = 0, ϕ 2 (J) = J 2 ), a ϕ ∅ -2-absorbing ideal (resp., ϕ 0 -2-absorbing ideal, ϕ 2 -2-absorbing ideal) is a 2-absorbing ideal (resp., weakly 2-absorbing ideal, almost 2-absorbing ideal).We show that ϕ-2-absorbing ideals enjoy analogs of many of the properties of 2-absorbing ideals.