Vogel's notion of regularity for non-coherent rings

Details Vogel's notion of regularity for non-coherent rings Vogel's notion of regularity for non-coherent rings

2006-12-19

arxiv.org/abs/math/0612569v1

Mathematics

K-Theory and Homology

19 pages, 3 figures. See also http://www.institut.math.jussieu.fr/~bihler

Scientific paper

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.

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