# Institute of Mathematics

## $(\delta,2)$-primary ideals of a commutative ring

#### Gülşen Ulucak, Ece Yetkin Çelikel

###### Received March, 2019.   Published online April 17, 2020.

Abstract:  Let $R$ be a commutative ring with nonzero identity, let $\mathcal{I(R)}$ be the set of all ideals of $R$ and $\delta\colon\mathcal{I(R)}\rightarrow\mathcal{I(R)}$ an expansion of ideals of $R$ defined by $I\mapsto\delta(I)$. We introduce the concept of $(\delta,2)$-primary ideals in commutative rings. A proper ideal $I$ of $R$ is called a $(\delta,2)$-primary ideal if whenever $a,b\in R$ and $ab\in I$, then $a^2\in I$ or $b^2\in\delta(I)$. Our purpose is to extend the concept of $2$-ideals to $(\delta,2)$-primary ideals of commutative rings. Then we investigate the basic properties of $(\delta,2)$-primary ideals and also discuss the relations among $(\delta,2)$-primary, $\delta$-primary and $2$-prime ideals.
Keywords:  $(\delta,2)$-primary ideal; $2$-prime ideal; $\delta$-primary ideal
Classification MSC:  13A15, 13F05, 05A15, 13G05
DOI:  10.21136/CMJ.2020.0146-19

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Affiliations:   Gülşen Ulucak, Department of Mathematics, Faculty of Science, Gebze Technical University, Gebze, Kocaeli, Turkey, e-mail: gulsenulucak@gtu.edu.tr; Ece Yetkin Çelikel (corresponding author), Department of Electrical Electronics Engineering, Faculty of Engineering, Hasan Kalyoncu University, Gaziantep, Turkey, e-mail: yetkinece@gmail.com, ece.celikel@hku.edu.tr

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