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

We prove the vanishing of the Koszul homology group Hμ(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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Bibliographic Details
Published in:Arkiv för matematik 2007-10, Vol.45 (2), p.273-278
Main Authors: Giral, José M., Planas-Vilanova, Francesc
Format: Article
Language:English
Subjects:
Commutativity
Homology
Modules
Rings (mathematics)
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Summary:We prove the vanishing of the Koszul homology group Hμ(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.
ISSN:0004-2080
1871-2487
DOI:10.1007/s11512-007-0043-z