Abstract
If R is a right coherent ring, then left R-modules have covers by submodules of flat R-modules if and only if all injective left R-modules have flat covers. This is the case if R is commutative and noetherian. If, furthermore, the Krull dimension of R is finite, then all cotorsion R-modules have flat covers. In this case, if F is a flat R-module, then F[[ x]] is a flat R[[ x]]-module.
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