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

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

2009-07-15

arxiv.org/abs/0907.2604v1

Mathematics

Commutative Algebra

9 pages, to appear in Proceedings of the AMS

Scientific paper

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
$\ell_A(F/N)$. Moreover, we prove that once the equality $\ell_A(F/N)=e(F/N)$
holds true for some parameter module $N$ in $F$, then the base ring $A$ is
Cohen-Macaulay.

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