Let $k$ be a field, let $R$ be a $k$-algebra, let $\{ S_i \}_{i \in I}$ be an inverse system of $k$-algebras, and let $R \to S_i$ be a $k$-algebra homomorphism making $S_i$ into a flat $R$-module. Is it true that $R \to \varprojlim_i S_i$ is also flat?
2026-03-27 00:04:21.1774569861
Inverse limit of flat algebras is flat?
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