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Flatness and the Ore condition for rings

Author(s): Peter Teichner
Journal: Proc. Amer. Math. Soc. 131 (2003), 1977-1980.
MSC (2000): Primary 16S10
Posted: February 11, 2003
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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.

References:

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2.: P. Cohn, Skew Fields, Encyclopedia of Math., Vol. 57, Cambridge Univ. Press 1995. MR 97d:12003
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4.: O. Ore, Linear equations in non-commutative fields, Annals of Math. 34, 480-508, 1931.
5.: B. Stenström, Rings of Quotients, Grundlehren der math. Wissenschaften, Vol. 217, Springer-Verlag 1975. MR 52:10782


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