Let $\mathbb C[[x]]$ be the ring of formal power series in a single indeterminate $x$. Let $\mathbb C((x))$ be the field of formal Laurent series which can be seen as the fraction field of $\mathbb C[[x]]$. It is well known that $\mathbb C((x))$ is a flat $\mathbb C[[x]]$-module. Is $\mathbb C((x))$ flat over $\mathbb C$?
2026-04-01 15:00:16.1775055616
Is the field of formal Laurent series flat over the ground ring?
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The complex numbers are a field and all modules over fields are free, therefore flat.