| Title:
|
On $S$-Noetherian rings (English) |
| Author:
|
Liu, Zhongkui |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
55-60 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a commutative ring and $S\subseteq R$ a given multiplicative set. Let $(M,\le )$ be a strictly ordered monoid satisfying the condition that $0\le m$ for every $m\in M$. Then it is shown, under some additional conditions, that the generalized power series ring $[[R^{M,\le }]]$ is $S$-Noetherian if and only if $R$ is $S$-Noetherian and $M$ is finitely generated. (English) |
| Keyword:
|
$S$-Noetherian ring |
| Keyword:
|
generalized power series ring |
| Keyword:
|
anti-Archimedean multiplicative set |
| Keyword:
|
$S$-finite ideal |
| MSC:
|
16P40 |
| idZBL:
|
Zbl 1160.16307 |
| idMR:
|
MR2310124 |
| . |
| Date available:
|
2008-06-06T22:50:29Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108049 |
| . |
| 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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| . |
