On a theorem of lan hughes about division rings of fractions

Warren Dicks; Dolors Herbera; Javier Sánchez

doi:https://doi.org/10.1081/AGB-120027970

On a theorem of lan hughes about division rings of fractions

Warren Dicks, Dolors Herbera, Javier Sánchez

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

7 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1127-1149
Journal	Communications in Algebra
Volume	32
DOIs	https://doi.org/10.1081/AGB-120027970
Publication status	Published - 1 Dec 2004

Keywords

Division ring of fractions
Hughes-free
Locally indicable group

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T1 - On a theorem of lan hughes about division rings of fractions

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AU - Herbera, Dolors

AU - Sánchez, Javier

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N2 - 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.

AB - 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.

KW - Division ring of fractions

KW - Hughes-free

KW - Locally indicable group

U2 - https://doi.org/10.1081/AGB-120027970

DO - https://doi.org/10.1081/AGB-120027970

M3 - Article

VL - 32

SP - 1127

EP - 1149

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

ER -