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Generating non-Noetherian modules constructively

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Abstract.

In [6], Heitmann gives a proof of a Basic Element Theorem, which has as corollaries some versions of the ‘‘Splitting-off’’ theorem of Serre and the Forster-Swan theorem in a non Noetherian setting. We give elementary and constructive proofs of such results. We introduce also a new notion of dimension for rings, which is only implicit in [6] and we present a generalisation of the Forster-Swan theorem, answering a question left open in [6].

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Authors and Affiliations

  1. Computing Science Department, Chalmers University of Technology, 41296, Göteborg, Sweden

    Thierry Coquand

  2. Equipe de Mathématiques, UMR CNRS 6623, UFR des Sciences et Techniques, Université de Franche-Comté, 25030, BESANCON Cedex, France

    Henri Lombardi

  3. Laboratoire de Mathématiques, SP2MI, Boulevard 3, Teleport 2, BP 179, 86960, FUTUROSCOPE Cedex, France

    Claude Quitté

Authors
  1. Thierry Coquand
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  2. Henri Lombardi
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  3. Claude Quitté
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Correspondence to Thierry Coquand.

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AcknowledgementWe thank the referee for his careful reading of this paper.

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Coquand, T., Lombardi, H. & Quitté, C. Generating non-Noetherian modules constructively. manuscripta math. 115, 513–520 (2004). https://doi.org/10.1007/s00229-004-0509-2

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  • DOI: https://doi.org/10.1007/s00229-004-0509-2

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