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

@article{Ulucak2020,
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.},
author = {Ulucak, Gülşen, Çelikel, Ece Yetkin},
journal = {Czechoslovak Mathematical Journal},
keywords = {$(\delta ,2)$-primary ideal; $2$-prime ideal; $\delta $-primary ideal},
language = {eng},
number = {4},
pages = {1079-1090},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$(\delta , 2)$-primary ideals of a commutative ring},
url = {http://eudml.org/doc/297398},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Ulucak, Gülşen
AU - Çelikel, Ece Yetkin
TI - $(\delta , 2)$-primary ideals of a commutative ring
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 4
SP - 1079
EP - 1090
AB - 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.
LA - eng
KW - $(\delta ,2)$-primary ideal; $2$-prime ideal; $\delta $-primary ideal
UR - http://eudml.org/doc/297398
ER -