Abstract
Let R be a commutative ring with 1 ≠ 0. A proper ideal I of R is a semiprimary ideal of R if whenever a, b ϵ R and ab ϵ I, we have [Formula: see text] or [Formula: see text]; and I is a weakly semiprimary ideal of R if whenever a, b ϵ R and 0 ≠ ab ϵ I, we have [Formula: see text] or [Formula: see text]. In this paper, we introduce a new class of ideals that is closely related to the class of (weakly) semiprimary ideals. Let I(R) be the set of all ideals of R and let [Formula: see text] 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. Then a proper ideal I of R is called a δ-semiprimary (weakly δ-semiprimary) ideal of R if ab ϵ I (0 ≠ ab ϵ I) implies a ϵ δ(I) or b ϵ δ(I). A number of results concerning weakly δ-semiprimary ideals and examples of weakly δ-semiprimary ideals are given.