Let G be a locally indicable group, K a division ring, and KG a crossed-product group ring. In 1961, Ian Hughes proved that, up to KG-isomorphism, at most one division ring of fractions of KG satisfies a certain independence condition, now called Hughes freeness. This result was applied by others in work on division rings of fractions of group rings of free groups. In this article, we introduce concepts that illuminate Hughes' arguments, and we simplify the proof of the theorem. Copyright © 2004 by Marcel Dekker, Inc.
- Division ring of fractions
- Locally indicable group