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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove the following result on the universal localization of a ring at an ideal : If the universal localization is flat as an -module, then satisfies the Ore condition with respect to the multiplicative set of elements that become invertible modulo . 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.

**1.**T. Cochran, K. Orr and P. Teichner,*Knot concordance, Whitney Towers, and**-signatures*, Preprint 1999, math.GT/9908117; to appear in Annals of Math.**2.**P. M. Cohn,*Skew fields*, Encyclopedia of Mathematics and its Applications, vol. 57, Cambridge University Press, Cambridge, 1995. Theory of general division rings. MR**1349108****3.**Julien Duval,*Forme de Blanchfield et cobordisme d’entrelacs bords*, Comment. Math. Helv.**61**(1986), no. 4, 617–635 (French). MR**870709**, 10.1007/BF02621935**4.**O. Ore,*Linear equations in non-commutative fields*, Annals of Math. 34, 480-508, 1931.**5.**Bo Stenström,*Rings of quotients*, Springer-Verlag, New York-Heidelberg, 1975. Die Grundlehren der Mathematischen Wissenschaften, Band 217; An introduction to methods of ring theory. MR**0389953**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
16S10

Retrieve articles in all journals with MSC (2000): 16S10

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