Proposition 63.31.5. If $\Lambda$ is Noetherian then $C(\Lambda )$ is a finitely generated $\Lambda$-module. Moreover, if $\Lambda$ is a field with prime subfield $\mathbf{F} \subset \Lambda$ then

$C(\Lambda )=(C(\mathbf{F}))\otimes _{\mathbf{F}}\Lambda$

compatibly with $T_ v$ acting.

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