The ring D(G) derived from the group ring KG is shown to possess exact
ly one pseudo-rank function in case G is an infinite, but locally and
residually finite. group and K is a field. The function is described n
aturally as the limit of the sequence of normalized ranks of all appro
ximation matrices. This fact is applied to an investigation of the dir
ect finiteness of the maximal quotient ring of D(G).