On S-(δ, 2)-primary ideals of a commutative ring
摘要
Let R be a commutative ring with identity, S be a multiplicative set of R, Id(R) be the set of all ideals of R, and δ: Id(R) → Id(R) be a function. Then δ is called an expansion function of ideals of R if whenever L, I, J are ideals of R with J ⊆ I, we have L ⊆ δ(L) and δ(J) ⊆ δ(I). Let δ be an expansion function of ideals of R. We introduce the concept of S-(δ, 2)-primary ideal which is a generalization of (δ, 2)-primary ideal. Let P be a proper ideal of R disjoint with S. We say that P is an S-(δ, 2)-primary ideal of R if there exists s ∈ S such that for all a, b ∈ R, if ab ∈ P, then sa2 ∈ P or sb2 ∈ δ(P). We next study the possible transfer of the above ideal property to the direct product of rings, quotient rings, localizations, trivial ring extensions, and amalgamation rings along an ideal.