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A note on the Buchsbaum-Rim multiplicity of a parameter module
Author(s):
Futoshi
Hayasaka;
Eero
Hyry
Journal:
Proc. Amer. Math. Soc.
138
(2010),
545-551.
MSC (2000):
Primary 13H15;
Secondary 13D25
Posted:
September 29, 2009
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Abstract:
In this article we prove that the Buchsbaum-Rim multiplicity  of a parameter module  in a free module  is bounded above by the colength  . Moreover, we prove that once the equality  holds true for some parameter module  in  , then the base ring  is Cohen-Macaulay.
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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
DOI:
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
Posted:
September 29, 2009
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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