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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Big Cohen-Macaulay algebras and seeds
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by Geoffrey D. Dietz PDF
Trans. Amer. Math. Soc. 359 (2007), 5959-5989 Request permission

Abstract:

In this article, we delve into the properties possessed by algebras, which we have termed seeds, that map to big Cohen-Macaulay algebras. We will show that over a complete local domain of positive characteristic any two big Cohen-Macaulay algebras map to a common big Cohen-Macaulay algebra. We will also strengthen Hochster and Huneke’s “weakly functorial" existence result for big Cohen-Macaulay algebras by showing that the seed property is stable under base change between complete local domains of positive characteristic. We also show that every seed over a positive characteristic ring $(R,m)$ maps to a balanced big Cohen-Macaulay $R$-algebra that is an absolutely integrally closed, $m$-adically separated, quasilocal domain.
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Additional Information
  • Geoffrey D. Dietz
  • Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019-0315
  • Address at time of publication: Department of Mathematics, Gannon University, Erie, Pennsylvania 16541
  • MR Author ID: 701237
  • Email: gdietz@member.ams.org
  • Received by editor(s): August 22, 2005
  • Published electronically: June 26, 2007
  • Additional Notes: The author was supported in part by a VIGRE grant from the National Science Foundation.
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 5959-5989
  • MSC (2000): Primary 13C14, 13A35; Secondary 13H10, 13B99
  • DOI: https://doi.org/10.1090/S0002-9947-07-04252-3
  • MathSciNet review: 2336312