DIVISION RINGS AND GROUP VON-NEUMANN-ALGEBRAS

Let G be a discrete group, let W(G) denote the group von Neumann algebra of G, and let U(G) denote the set of closed densely defined linear operators affiliated to W(G). If G is torsion free and has a normal free subgroup H such that G/H is elementary amenable, then we shall prove that there exists a division ring D such that CG subset-or-equal-to D subset-or-equal-to U(G). For G as above, this will establish the integrality of numbers arising from L2-cohomology associated with G.