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Flatness and the Ore condition for rings


Author: Peter Teichner
Journal: Proc. Amer. Math. Soc. 131 (2003), 1977-1980
MSC (2000): Primary 16S10
Published electronically: February 11, 2003
MathSciNet review: 1963739
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06975-2
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
Article copyright: © Copyright 2003 American Mathematical Society