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Die Verallgemeinerung eines Satzes von Bourbaki und einige Anwendungen

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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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Literatur

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Authors and Affiliations

  1. Institut für Mathematik der Technischen Universität, Erzstr. 1, D-3392, Clausthal-Zellerfeld

    Winfried Bruns & Udo Vetter

Authors
  1. Winfried Bruns
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  2. Udo Vetter
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Bruns, W., Vetter, U. Die Verallgemeinerung eines Satzes von Bourbaki und einige Anwendungen. Manuscripta Math 17, 317–325 (1975). https://doi.org/10.1007/BF01170728

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  • DOI: https://doi.org/10.1007/BF01170728

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