Title: On an analogue of L2-Betti numbers for finite field coefficients and a question of Atiyah
Abstract: We construct a dimension function for modules over the group ring of an amenable group. This may replace the von Neumann dimension in the definition of L2-Betti numbers and thus allows an analogue definition for finite field coefficients. Furthermore we construct examples for characteristic 2 in answer to Atiyah question of irrational L2-Betti numbers.