ON RINGS OF QUOTIENTS OF GROUP-ALGEBRAS OF SOLUBLE GROUPS OF FINITE RANK

Let F be a field and G a finite extension of a torsion-free soluble group of finite rank such that the characteristic of F does not lie in the spectrum of G. The group algebra FG has a classical ring D of quotients. We prove that D is locally residually finite-dimensional over F. There are a number of corollaries. Our results hold more generally. For example, G could also be any soluble-by-finite linear group over the rationals or any metabelian group with torsion-free derived subgroup.