Journal of Symbolic Logic

Division rings whose vector spaces are pseudofinite

Vinicius Cifú Lopes and Lou van den Dries

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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.

Article information

Source
J. Symbolic Logic, Volume 75, Issue 3 (2010), 1087-1090.

Dates
First available in Project Euclid: 9 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1278682217

Digital Object Identifier
doi:10.2178/jsl/1278682217

Mathematical Reviews number (MathSciNet)
MR2723784

Zentralblatt MATH identifier
1201.03021

Citation

Dries, Lou van den; Cifú Lopes, Vinicius. Division rings whose vector spaces are pseudofinite. J. Symbolic Logic 75 (2010), no. 3, 1087--1090. doi:10.2178/jsl/1278682217. https://projecteuclid.org/euclid.jsl/1278682217


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