The generating hypothesis in the derived category of a ring

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dc.creatorHovey, Mark
dc.creatorLockridge, Keir
dc.creatorPuninski, Gena
dc.date2006-10-05
dc.date.accessioned2026-07-07T07:28:46Z
dc.date.available2026-07-07T07:28:46Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/math/0610201
dc.identifierhttp://arxiv.org/abs/math/0610201
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117857
dc.subjectAlgebraic Topology
dc.subjectCategory Theory
dc.subjectRings and Algebras
dc.subject55U35; 18E30; 16E50
dc.titleThe generating hypothesis in the derived category of a ring
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