A note on the Buchsbaum-Rim multiplicity of a parameter module
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- by Futoshi Hayasaka and Eero Hyry PDF
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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.References
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Additional Information
- 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
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 545-551
- MSC (2000): Primary 13H15; Secondary 13D25
- DOI: https://doi.org/10.1090/S0002-9939-09-10119-3
- MathSciNet review: 2557171