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arXiv · 0907.2604

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

Futoshi Hayasaka·Eero Hyry
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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 $\ell_A(F/N)$. 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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Futoshi Hayasaka, Eero Hyry. 2009-07-15. A Note on the Buchsbaum-Rim multiplicity of a parameter module. https://arxiv.org/abs/0907.2604

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