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

 

The Dedekind-Mertens formula
and determinantal rings


Authors: Winfried Bruns and Anna Guerrieri
Journal: Proc. Amer. Math. Soc. 127 (1999), 657-663
MSC (1991): Primary 13C40, 13C14, 13D40, 13P10
MathSciNet review: 1468185
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Abstract: We give a combinatorial proof of the Dedekind-Mertens formula by computing the initial ideal of the content ideal of the product of two generic polynomials. As a side effect we obtain a complete classification of the rank $1$ Cohen-Macaulay modules over the determinantal rings $K[X]/I_2(X)$.


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Additional Information

Winfried Bruns
Affiliation: Universität Osnabrück, FB Mathematik/Informatik, 49069 Osnabrück, Germany
Email: Winfried.Bruns@mathematik.uni-osnabrueck.de

Anna Guerrieri
Affiliation: Universität Osnabrück, FB Mathematik/Informatik, 49069 Osnabrück, Germany
Email: guerran@univaq.it

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04535-9
PII: S 0002-9939(99)04535-9
Keywords: Dedekind--Mertens formula, initial ideal, determinantal ring, Cohen--Macaulay module
Received by editor(s): January 22, 1997
Received by editor(s) in revised form: June 16, 1997
Additional Notes: The visit of the first author to the University of L’Aquila that made this paper possible was supported by the Vigoni program of the DAAD and the CRUI
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1999 American Mathematical Society