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arXiv · 1206.4523

Über die assoziierten Primideale der Vervollständigung

Helmut Zöschinger
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Abstract

Let $(R,\my)$ be a noetherian local ring and let $M$ be an $R$-module such that $\bigcap\limits_{n\geq 1} \my^n M=0.$ Let $\hat{M}$ be the completion of $M$. We show that Ass$(\hat{M})=$ Koatt$(M)$ holds in the following three cases: if $\dim(R)\leq 1,$ if $\hat{M}$ as $R$-module is flat, or if $M$ is the direct sum of $R$-modules which are finitely generated. If $M$ is pure in $\hat{M}$ then at least Ass$(\hat{M}) \subset $ Koatt$(M)$ holds. If the conjecture by A.-M.Simon on complete $R$-modules is valid then one has Koatt$(M)\subset $ Ass$(\hat{M}).$

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Helmut Zöschinger. 2012-06-20. Über die assoziierten Primideale der Vervollständigung. https://arxiv.org/abs/1206.4523

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