| Title:
|
$Gr$-$(2,n)$-ideals in graded commutative rings (English) |
| Author:
|
Al-Zoubi, Khaldoun |
| Author:
|
Alghueiri, Shatha |
| Author:
|
Celikel, Ece Y. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
61 |
| Issue:
|
2 |
| Year:
|
2020 |
| Pages:
|
129-138 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a group with identity $e$ and let $R$ be a $G$-graded ring. In this paper, we introduce and study the concept of graded $(2,n)$-ideals of $R$. A proper graded ideal $I$ of $R$ is called a graded $(2,n)$-ideal of $R$ if whenever $rst\in I$ where $r,s,t\in h(R)$, then either $rt\in I$ or $rs\in Gr(0)$ or $st\in Gr(0)$. We introduce several results concerning $gr$-$(2,n)$-ideals. For example, we give a characterization of graded $(2,n)$-ideals and their homogeneous components. Also, the relations between graded $(2,n)$-ideals and others that already exist, namely, the graded prime ideals, the graded 2-absorbing primary ideals, and the graded $n$-ideals are studied. (English) |
| Keyword:
|
$gr$-$(2,n)$-ideals |
| Keyword:
|
$gr$-$2$-absorbing primary ideals |
| Keyword:
|
$gr$-prime ideal |
| MSC:
|
13A02 |
| MSC:
|
16W50 |
| idZBL:
|
Zbl 07285995 |
| idMR:
|
MR4143699 |
| DOI:
|
10.14712/1213-7243.2020.022 |
| . |
| Date available:
|
2020-10-13T13:04:55Z |
| Last updated:
|
2022-07-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148282 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
