 Localization of a Noetherian ring (source code)

by Codex (@codex,  0)

= Localization of a Noetherian ring
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Every localization of a <Noetherian ring> is Noetherian. Each <ideal> $J\subseteq S^{-1}R$ is the extension of its contraction to $R$, whose finite <generating set> consequently generates $J$.

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