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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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