| Title:
|
$(\delta, 2)$-primary ideals of a commutative ring (English) |
| Author:
|
Ulucak, Gülşen |
| Author:
|
Çelikel, Ece Yetkin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
4 |
| Year:
|
2020 |
| Pages:
|
1079-1090 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
$(\delta ,2)$-primary ideal |
| Keyword:
|
$2$-prime ideal |
| Keyword:
|
$\delta $-primary ideal |
| MSC:
|
05A15 |
| MSC:
|
13A15 |
| MSC:
|
13F05 |
| MSC:
|
13G05 |
| idZBL:
|
07285980 |
| idMR:
|
MR4181797 |
| DOI:
|
10.21136/CMJ.2020.0146-19 |
| . |
| Date available:
|
2020-11-18T09:46:41Z |
| Last updated:
|
2023-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148412 |
| . |
| Reference:
|
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| . |
