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Induktive Limiten endlich erzeugter freier Moduln

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Abstract

If X is a set, R a ring and M an R-module, then it is shown that the R-module of all M-valued functions on X taking on X only finitely many values is free over R. This result is applied to show that inductive limits of finitely generated free R-modules are free over R, provided that the mappings of the inductive system are of a certain ‘diagonal’ type. No restrictions are placed on the index set. There is a dual statement for projective limits. Among other applications it is shown that the -1st Borel-Moore homology group (with values in any sheaf over an arbitrary integral domain and taken with respect to any paracompactifying family of supports) of a locally compact space vanishes.

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Literatur

  1. BOREL, A. and J.C. MOORE: Homology theory for locally compact spaces. Mich.Math.J.7, 137–159 (1960).

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  2. BREDON, G. E.: Sheaf theory. McGraw-Hill (1967).

  3. CHASE, S.: Proc. Symp. Abelian Groups, Scott Foresman and Co. (1963).

  4. NÖBELING, G.: Verallgemeinerung eines Satzes von Herrn Specker. Invent.Math. 6, 41–55 (1968).

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  5. SPECKER, E.: Additive Gruppen von Folgen ganzer Zahlen. Port.Math.9, 131–140 (1950).

    Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstr. 1 1|2, D-852, Erlangen

    Ludger Kaup

  2. Dept. of Mathematics, Yale University, 06520, New Haven, Ct., USA

    Michael S. Keane

Authors
  1. Ludger Kaup
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  2. Michael S. Keane
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Kaup, L., Keane, M.S. Induktive Limiten endlich erzeugter freier Moduln. Manuscripta Math 1, 9–21 (1969). https://doi.org/10.1007/BF01171131

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  • DOI: https://doi.org/10.1007/BF01171131

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