REGULAR SKEW GROUP-RINGS

Let G be a group acting on a ring R. We study the problem of determini ng necessary and sufficient conditions in order that the skew group ri ng RG be von Neumann regular. Complete characterizations are given in some particular situations, including the case where all idempotents o f R are central. For a regular ring R admitting a G-invariant pseudo-r ank function N, with G finite, we obtain a necessary condition for RG being regular in terms of the induced action of G on the N-completion of R.