The generating hypothesis in the derived category of a ring |
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Authors: | Mark Hovey Keir Lockridge Gena Puninski |
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Institution: | (1) Department of Mathematics, Wesleyan University, Middletown, CT 06459, USA;(2) Department of Mathematics, University of Manchester, Booth Street East, Manchester, M13 PL, UK |
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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 (J. Pure Appl. Algebra 208(2), 2007). 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. |
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