Geodesic
On $S$-Noetherian rings
Archivum mathematicum, Tome 43 (2007) no. 1, pp. 55-60 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 16P40
Keywords: $S$-Noetherian ring; generalized power series ring; anti-Archimedean multiplicative set; $S$-finite ideal 
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     author = {Liu, Zhongkui},
     title = {On $S${-Noetherian} rings},
     journal = {Archivum mathematicum},
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     mrnumber = {2310124},
     zbl = {1160.16307},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2007_43_1_a4/}
}
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Liu, Zhongkui. On $S$-Noetherian rings. Archivum mathematicum, Tome 43 (2007) no. 1, pp. 55-60. http://geodesic.mathdoc.fr/item/ARM_2007_43_1_a4/

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