In Theorem 6 of [1], if R is a von Neumann regular ring, then every 2-prime ideal of R is a prime ideal. But the converse of this implication does not hold. Thus, we correct Theorem 6 of [1] as follows: Theorem 6. Let R be a ring. If R is von Neumann regular, then every 2-prime ideal of R is a prime ideal. P r o o f . © 2020, Mathematical Institute, Academy of Sciences of Cz

Ulucak, Gülşen

Yetkin Çelikel, Ece

Let R be a commutative ring with nonzero identity, let I(R) be the set of all ideals of R and δ: I(R) → I(R) an expansion of ideals of R defined by I ↦ δ(I). We introduce the concept of (δ, 2)-primary ideals in commutative rings. A proper ideal I of R is called a (δ, 2)-primary ideal if whenever a, b ∈ R and ab ∈ I, then a2 ∈ I or b2 ∈ δ(I). Our purpose is to extend the concept of 2-ideals to (δ, 2)-primary ideals of commutative rings. Then we investigate the basic properties of (δ, 2)-primary ideals and also discuss the relations among (δ, δ-primary, δ-primary and 2-prime ideals. © 2020, Mathematical Institute, Academy of Sciences of Cz

Çelikel, Ece Yetkin

DSpace@HKU

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(δ, 2)-Primary Ideals of a Commutative Ring

Institute of Mathematics AS CR, v. v. i.

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

summary: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

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

Czech digital mathematics library

http://openaccess.hku.edu.tr/xmlui/bitstream/20.500.11782/2174/1/10.21136CMJ.2020.0146-19.pdf

Erratum to (δ, 2)-Primary Ideals of a Commutative Ring (Czechoslovak Mathematical Journal, (2020), 70, 4, (1079-1090), 10.21136/CMJ.2020.0146-19)

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DSpace@HKU

Institute of Mathematics AS CR, v. v. i.

Institute of Mathematics AS CR, v. v. i.

Czech digital mathematics library

Czech digital mathematics library

DSpace@HKU