Abstract:  Let  R  be a ring, let  F  be a free group, and let  X  be a basis of  F.
    Let  \epsilon: RF -> R denote the usual augmentation map for the group ring  RF,
let X\partial:= {x-1 | x \in X} \subseteq RF, let  \Sigma  denote the set of matrices
over  RF  that are sent to invertible matrices by  \epsilon, and let  (RF)\Sigma^-1  denote
the universal localization of  RF  at  \Sigma.
     A classic result of Magnus and Fox gives an embedding of  RF  in a 
power-series ring  R<<X\partial>>.  We show that if  R  is a commutative Bezout domain,
then the division closure of the image of  RF  in  R<<X\partial>>  is a universal
localization of  RF  at  \Sigma.
     We also show that  (RF)\Sigma^-1  is stably flat as an  RF-ring, in the sense of
Neeman-Ranicki, whenever  R is a von neumann regular ring or a commutative
Bezout domain.

March 31, 2006 version, 12 pages, available as
 

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