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

Ulucak, Gülşen ; Çelikel, Ece Yetkin

Czechoslovak Mathematical Journal, Tome 70 (2020) no. 4, pp. 1079-1090.

Résumé

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.

Détail

DOI : 10.21136/CMJ.2020.0146-19

Classification : 05A15, 13A15, 13F05, 13G05
Keywords: $(\delta, 2)$-primary ideal; $2$-prime ideal; $\delta $-primary ideal