Vogel's notion of regularity for non-coherent rings, by Frank Bihler

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.

Frank Bihler <bihler@math.jussieu.fr>