The generating hypothesis in the derived category of R-modules

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dc.creatorLockridge, Keir H.
dc.date2005-11-21
dc.date.accessioned2026-07-07T06:51:34Z
dc.date.available2026-07-07T06:51:34Z
dc.descriptionIn this paper, we prove a version of Freyd's generating hypothesis for triangulated categories: if D is a cocomplete triangulated category and S is an object in D whose endomorphism ring is graded commutative and concentrated in degree zero, then S generates (in the sense of Freyd) the thick subcategory determined by S if and only if the endomorphism ring of S is von Neumann regular. As a corollary, we obtain that the generating hypothesis is true in the derived category of a commutative ring R if and only if R is von Neumann regular. We also investigate alternative formulations of the generating hypothesis in the derived category. Finally, we give a characterization of the Noetherian stable homotopy categories in which the generating hypothesis is true.
dc.description16 pages, submitted to JPAA
dc.identifierhttps://arxiv.org/abs/math/0511534
dc.identifierhttp://arxiv.org/abs/math/0511534
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/105027
dc.subjectAlgebraic Topology
dc.subject55p42; 18e30
dc.titleThe generating hypothesis in the derived category of R-modules
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