2-absorbing δ-semiprimary Ideals of Commutative Rings

Abstract

Let R be a commutative ring with nonzero identity, I(R) the set of all idealsof R and δ: I(R) → I(R) an expansion of ideals of R. In this paper, we introduce theconcept of 2-absorbing δ-semiprimary ideals in commutative rings which is an extensionof 2-absorbing ideals. A proper ideal I of R is called 2-absorbing δ-semiprimary idealif whenever a, b, c ∈ R and abc ∈ I, then either ab ∈ δ(I) or bc ∈ δ(I) or ac ∈ δ(I).Many properties and characterizations of 2-absorbing δ-semiprimary ideals are obtained.Furthermore, 2-absorbing δ1-semiprimary avoidance theorem is proved © Kyungpook Mathematical Journal