| Abstrakt: |
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. |
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