On -Noetherian rings
Archivum Mathematicum (2007)
- Volume: 043, Issue: 1, page 55-60
- ISSN: 0044-8753
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topLiu, Zhongkui. "On $S$-Noetherian rings." Archivum Mathematicum 043.1 (2007): 55-60. <http://eudml.org/doc/250166>.
@article{Liu2007,
abstract = {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.},
author = {Liu, Zhongkui},
journal = {Archivum Mathematicum},
keywords = {$S$-Noetherian ring; generalized power series ring; anti-Archimedean multiplicative set; $S$-finite ideal; Noetherian rings; generalized power series rings; strictly ordered monoids},
language = {eng},
number = {1},
pages = {55-60},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On $S$-Noetherian rings},
url = {http://eudml.org/doc/250166},
volume = {043},
year = {2007},
}
TY - JOUR
AU - Liu, Zhongkui
TI - On $S$-Noetherian rings
JO - Archivum Mathematicum
PY - 2007
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 043
IS - 1
SP - 55
EP - 60
AB - 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.
LA - eng
KW - $S$-Noetherian ring; generalized power series ring; anti-Archimedean multiplicative set; $S$-finite ideal; Noetherian rings; generalized power series rings; strictly ordered monoids
UR - http://eudml.org/doc/250166
ER -
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