RANK-FUNCTIONS ON RINGS DERIVED FROM GROUP-RINGS

The ring D(G) derived from the group ring KG is shown to possess exactly 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 naturally as the limit of the sequence of normalized ranks of all approximation matrices. This fact is applied to an investigation of the direct finiteness of the maximal quotient ring of D(G).