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On S -Noetherian rings

Zhongkui Liu (2007)

Archivum Mathematicum

Let R be a commutative ring and S R a given multiplicative set. Let ( M , ) be a strictly ordered monoid satisfying the condition that 0 m for every m M . Then it is shown, under some additional conditions, that the generalized power series ring [ [ R M , ] ] is S -Noetherian if and only if R is S -Noetherian and M is finitely generated.

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