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http://dx.doi.org/10.5666/KMJ.2021.61.4.711

2-absorbing δ-semiprimary Ideals of Commutative Rings  

Celikel, Ece Yetkin (Department of Electrical-Electronics Engineering, Faculty of Engineering, Hasan Kalyoncu University)
Publication Information
Kyungpook Mathematical Journal / v.61, no.4, 2021 , pp. 711-725 More about this Journal
Abstract
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.
Keywords
2-absorbing ${\delta}$-primary ideal; ${\delta}$-primary ideal; ${\delta}$-semiprimary ideal; 2-absorbing ideal; 2-absorbing primay ideal;
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Times Cited By KSCI : 2  (Citation Analysis)
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