What question did this study set out to answer?

This work aims to define and explore the concept of 2-absorbing delta-semiprimary ideals in commutative rings.

February 2, 2026Open Access

2-absorbing ?-semiprimary Ideals of Commutative Rings

Key Points

This work aims to define and explore the concept of 2-absorbing delta-semiprimary ideals in commutative rings.
Definition of 2-absorbing delta-semiprimary ideals
Exploration of conditions for ideals based on products of ring elements
Analysis of properties and characterizations of these ideals
Proof of the 2-absorbing delta1-semiprimary avoidance theorem
Introduction of the concept of 2-absorbing delta-semiprimary ideals
Establishment of various properties related to these ideals
Characterizations that provide deeper insights into their structure
Successful proof of the avoidance theorem for 2-absorbing delta1-semiprimary ideals

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

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