Le théorème de Skolem-Noether pour les modules sur des anneaux principaux

Anne Cortella[1]; Jean-Pierre Tignol[2]

  • [1] UMR CNRS 6623, Laboratoire de Mathématiques Université de Franche-Comté 16 route de Gray F-25030 Besançon Cedex, France
  • [2] Département de Mathématiques Université Catholique de Louvain B-1348 Louvain-la-Neuve, Belgique

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 2, page 511-516
  • ISSN: 1246-7405

Abstract

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Let k be a principal ideal domain and M a torsion k -module of finite type. We give an elementary proof of the fact that any k -algebra automorphism of R = End k M is inner.

How to cite

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Cortella, Anne, and Tignol, Jean-Pierre. "Le théorème de Skolem-Noether pour les modules sur des anneaux principaux." Journal de Théorie des Nombres de Bordeaux 17.2 (2005): 511-516. <http://eudml.org/doc/249424>.

@article{Cortella2005,
abstract = {Soit $k$ un anneau principal et $M$ un $k$-module de torsion de type fini. Nous donnons une preuve élémentaire du fait que tout automorphisme de $k$-algèbre de $R=\operatorname\{End\}_\{k\}M$ est intérieur.},
affiliation = {UMR CNRS 6623, Laboratoire de Mathématiques Université de Franche-Comté 16 route de Gray F-25030 Besançon Cedex, France; Département de Mathématiques Université Catholique de Louvain B-1348 Louvain-la-Neuve, Belgique},
author = {Cortella, Anne, Tignol, Jean-Pierre},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {principal ideal domain; automorphism},
language = {fre},
number = {2},
pages = {511-516},
publisher = {Université Bordeaux 1},
title = {Le théorème de Skolem-Noether pour les modules sur des anneaux principaux},
url = {http://eudml.org/doc/249424},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Cortella, Anne
AU - Tignol, Jean-Pierre
TI - Le théorème de Skolem-Noether pour les modules sur des anneaux principaux
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 2
SP - 511
EP - 516
AB - Soit $k$ un anneau principal et $M$ un $k$-module de torsion de type fini. Nous donnons une preuve élémentaire du fait que tout automorphisme de $k$-algèbre de $R=\operatorname{End}_{k}M$ est intérieur.
LA - fre
KW - principal ideal domain; automorphism
UR - http://eudml.org/doc/249424
ER -

References

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