Let R be a commutative ring with nonzero identity, let I(R) be the set of all ideals of R and δ: I(R) → I(R) an expansion of ideals of R defined by I ↦ δ(I). We introduce the concept of (δ, 2)-primary ideals in commutative rings. A proper ideal I of R is called a (δ, 2)-primary ideal if whenever a, b ∈ R and ab ∈ I, then a² ∈ I or b² ∈ δ(I). Our purpose is to extend the concept of 2-ideals to (δ, 2)-primary ideals of commutative rings. Then we investigate the basic properties of (δ, 2)-primary ideals and also discuss the relations among (δ, δ-primary, δ-primary and 2-prime ideals.

中文翻译：

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（δ，2）-交换环的基本理想

让- [R是具有非零身份交换环，让我（[R ）是集合的全部理想的[R和δ：我（[R）→我（[R ）的的理想的膨胀- [R由下式定义我↦ δ（我）。我们介绍了交换环中（δ，2）-初等理想的概念。一个适当的理想我的- [R被称为（δ，2）-primary理想的，如果每当A，B ∈ [R和AB ∈余，则一个² ∈我或b ² ∈ δ（我）。我们的目的是将2理想的概念扩展到交换环的（δ，2）初等理想。然后，我们研究了（δ，2）理想的基本性质，并讨论了（δ，δ-初等，δ-初等和2理想之间的关系。