A Note on the Buchsbaum-Rim multiplicity of a parameter module

2009/07/15 by Futoshi Hayasaka, Hayasaka, Futoshi, Eero Hyry +1 · 1 citation
Mathematics · #13D25 #13H15 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13D25 #msc:13H15

paper · pdf · doi:10.48550/arxiv.0907.2604

9 pages, to appear in Proceedings of the AMS

arxiv created 2009/07/15 · arxiv updated 2009/12/01

Abstract

In this article we prove that the Buchsbaum-Rim multiplicity e(F/N) of a parameter module N in a free module F=A^r is bounded above by the colength ℓ_A(F/N). Moreover, we prove that once the equality ℓ_A(F/N)=e(F/N) holds true for some parameter module N in F, then the base ring A is Cohen-Macaulay.

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