A note on the acyclicity of the Koszul complex of a module

José M. Giral Departament d’Àlgebra i Geometria, Universitat de Barcelona Francesc Planas-Vilanova Departament de Matemàtica Aplicada 1, Universitat Politècnica de Catalunya

TBD mathscidoc:1701.333108

Arkiv for Matematik, 45, (2), 273-278, 2006.8
We prove the vanishing of the Koszul homology group$H$_{μ}(Kos($M$)_{μ}), where μ is the minimal number of generators of M. We give a counterexample that the Koszul complex of a module is not always acyclic and show its relationship with the homology of commutative rings.
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@inproceedings{josé2006a,
  title={A note on the acyclicity of the Koszul complex of a module},
  author={José M. Giral, and Francesc Planas-Vilanova},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203620192171917},
  booktitle={Arkiv for Matematik},
  volume={45},
  number={2},
  pages={273-278},
  year={2006},
}
José M. Giral, and Francesc Planas-Vilanova. A note on the acyclicity of the Koszul complex of a module. 2006. Vol. 45. In Arkiv for Matematik. pp.273-278. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203620192171917.
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