Vogel's notion of regularity for non-coherent rings

Abstract

We study the notion of regular ring in the sense of Vogel, which generalizes the classical notion for non-necessarily coherent rings. We build a class of groups "R" containing Waldhausen's class "Cl" in [Wald78] and study its stability results. We show that for a regular ring R and a group G in "R", the group ring R[G] is still regular. Finally, we state Vogel's excision conjecture generalizing Waldhausen's results in [Wald78] concerning Whitehead and KNil groups.