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September 2010 Division rings whose vector spaces are pseudofinite
Vinicius Cifú Lopes, Lou van den Dries
J. Symbolic Logic 75(3): 1087-1090 (September 2010). DOI: 10.2178/jsl/1278682217

Abstract

Vector spaces over fields are pseudofinite, and this remains true for vector spaces over division rings that are finite-dimensional over their center. We also construct a division ring such that the nontrivial vector spaces over it are not pseudofinite, using Richard Thompson's group F. The idea behind the construction comes from a first-order axiomatization of the class of division rings all whose nontrivial vector spaces are pseudofinite.

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Vinicius Cifú Lopes. Lou van den Dries. "Division rings whose vector spaces are pseudofinite." J. Symbolic Logic 75 (3) 1087 - 1090, September 2010. https://doi.org/10.2178/jsl/1278682217

Information

Published: September 2010
First available in Project Euclid: 9 July 2010

zbMATH: 1201.03021
MathSciNet: MR2723784
Digital Object Identifier: 10.2178/jsl/1278682217

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 3 • September 2010
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