Abstract
We generalize a theorem of Bourbaki: Let R be a noetherian ring and M a finitely generated torsionfree R-module with rank r. Assume further M to be free for all ∈ Spec R with depth ⩽ 1. Then there exists a free submodule F in M such that M/F is isomorphic to an ideal in R. There are some applications due to E.G.Evans,Jr. and M. Auslander, concerning the group Ko (R) resp. reflexive R-modules and - in case R is Gorenstein - R-modules of finite length.
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