Remark 15.90.9. If $R \to R^\wedge $ is flat, then for each positive integer $n$ tensoring the sequence $0 \to R[f^ n] \to R \to R$ with $R^\wedge $ gives the sequence $0 \to R[f^ n] \otimes _ R R^\wedge \to R^\wedge \to R^\wedge $. Combined with Lemma 15.90.2 we conclude that $R[f^ n] \to R^\wedge [f^ n]$ is an isomorphism. Thus $(R, f)$ is a glueing pair. This holds in particular if $R$ is Noetherian, see Algebra, Lemma 10.97.2.
Post a comment
Your email address will not be published. Required fields are marked.
In your comment you can use Markdown and LaTeX style mathematics (enclose it like
$\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
All contributions are licensed under the GNU Free Documentation License.