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Kyungpook Mathematical Journal 2021; 61(4): 711-725

Published online December 31, 2021

Copyright © Kyungpook Mathematical Journal.

2-absorbing δ-semiprimary Ideals of Commutative Rings

Ece Yetkin Çelikel

Department of Electrical-Electronics Engineering, Faculty of Engineering, Hasan Kalyoncu University, Gaziantep, Turkey
e-mail : ece.celikel@hku.edu.tr, yetkinece@gmail.com

Received: December 18, 2020; Accepted: May 18, 2021

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,cR and abcI, then either abδ(I) or bcδ(I) or acδ(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 δ-primary ideal, δ-primary ideal, δ-semiprimary ideal, 2-absorbing ideal, 2-absorbing primay ideal