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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Futoshi Hayasaka and Eero Hyry
Journal: Proc. Amer. Math. Soc. 138 (2010), 545-551
MSC (2000): Primary 13H15; Secondary 13D25
Published electronically: September 29, 2009
MathSciNet review: 2557171
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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
Affiliation: Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki 214–8571, Japan
Email: hayasaka@isc.meiji.ac.jp

Eero Hyry
Affiliation: Department of Mathematics and Statistics, University of Tampere, 33014 Tampereen yliopisto, Finland
Email: Eero.Hyry@uta.fi

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10119-3
PII: S 0002-9939(09)10119-3
Keywords: Buchsbaum-Rim multiplicity, parameter module, Euler-Poincar\'e characteristic, generalized Koszul complex
Received by editor(s): August 17, 2008
Received by editor(s) in revised form: July 14, 2009
Published electronically: September 29, 2009
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.