• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.193-198
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• 2017

In this paper we investigate 2-absorbing ${\delta}$-primary ideals which unify 2-absorbing ideals and 2-absorbing primary ideals. A number of results about 2-absorbing ideals and 2-absorbing primary ideals are extended into this general framework.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.711-725
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• 2021

Let R be a commutative ring with nonzero identity, 𝓘(𝓡) the set of all ideals of R and δ : 𝓘(𝓡) → 𝓘(𝓡) an expansion of ideals of R. In this paper, we introduce the concept of 2-absorbing δ-semiprimary ideals in commutative rings which is an extension of 2-absorbing ideals. A proper ideal I of R is called 2-absorbing δ-semiprimary ideal if 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.