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 | References | Similar Articles | Additional Information

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 Cohen-Macaulay modules over the determinantal rings .

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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

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