Covers by flat modules and submodules of flat modules
EE Enochs - Journal of Pure and Applied Algebra, 1989 - Elsevier
EE Enochs
Journal of Pure and Applied Algebra, 1989•ElsevierIf 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.
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.
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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