2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105154Let A denote the algebraic closure of the rationals Q in the complex numbers C. Suppose G is a torsion-free group which contains a congruence subgroup as a normal subgroup of finite index and denote by U(G) the C-algebra of closed densely defined unbounded operators affiliated to the group von Neumann algebra. We prove that there exists a division ring D(G) such that A[G] < D(G) < U(G). This establishes some versions of the Atiyah conjecture for the group G.Second version: 14 pages. Minor corrections and changes, some due to helpful comments by the refereeRings and AlgebrasFunctional AnalysisGeometric Topology16S34 (Primary) 20C07, 22D25, 46L99 (Secondary)text