Title: The generating hypothesis in the derived category of a ring.
Authors: Mark Hovey, Keir Lockridge, and Gena Puninski
Authors' email addresses: mhovey@wesleyan.edu, klockridge@wesleyan.edu, gpuninski@maths.manchester.ac.uk
Abstract:
We show that a strong form (the fully faithful version) of the generating
hypothesis, introduced by Freyd in algebraic topology, holds in the
derived category of a ring R if and only if R is von Neumann regular.
This extends results of the second author. We also characterize rings for
which the original form (the faithful version) of the generating
hypothesis holds in the derived category of R. These must be close to von
Neumann regular in a precise sense, and, given any of a number of
finiteness hypotheses, must be von Neumann regular. However, we construct
an example of such a ring that is not von Neumann regular, and therefore
does not satisfy the strong form of the generating hypothesis.