A note on the acyclicity of the Koszul complex of a module |
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| Authors: | José M Giral Francesc Planas-Vilanova |
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| Institution: | (1) Departament d’àlgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, ES-08007 Barcelona, Spain;(2) Departament de Matemàtica Aplicada 1, Universitat Politècnica de Catalunya, Diagonal 647, ETSEIB, ES-08028 Barcelona, Spain |
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| Abstract: | 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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