## The Dedekind-Mertens formula and determinantal rings

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- by Winfried Bruns and Anna Guerrieri PDF
- Proc. Amer. Math. Soc.
**127**(1999), 657-663 Request permission

## 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 $K[X]/I_2(X)$.## References

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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
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**127**(1999), 657-663 - MSC (1991): Primary 13C40, 13C14, 13D40, 13P10
- DOI: https://doi.org/10.1090/S0002-9939-99-04535-9
- MathSciNet review: 1468185