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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Flatness and the Ore condition for rings
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by Peter Teichner PDF
Proc. Amer. Math. Soc. 131 (2003), 1977-1980 Request permission

Abstract:

We prove the following result on the universal localization of a ring $R$ at an ideal $I$: If the universal localization is flat as an $R$-module, then $R$ satisfies the Ore condition with respect to the multiplicative set of elements that become invertible modulo $I$. It is well known that for domains the converse of this result holds, and hence we have found in this case a new characterization of the Ore condition.
References
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Additional Information
  • Peter Teichner
  • Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093-0112
  • Email: teichner@math.ucsd.edu
  • Received by editor(s): July 5, 2001
  • Published electronically: February 11, 2003
  • Additional Notes: This research was supported by the NSF, grant DMS0072775
  • Communicated by: Lance W. Small
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 1977-1980
  • MSC (2000): Primary 16S10
  • DOI: https://doi.org/10.1090/S0002-9939-03-06975-2
  • MathSciNet review: 1963739