## 2007.180: The generating hypothesis in the derived category of a ring

2007.180:
Mark Hovey, Keir Lockridge and Gena Puninski
(2007)
*The generating hypothesis in the derived category of a ring.*
Mathematische Zeitschrift, 256 (4).
pp. 789-800.
ISSN 1432-1823

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DOI: 10.1007/s00209-007-0103-x

## 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.

Item Type: | Article |
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Subjects: | MSC 2000 > 16 Associative rings and algebras |

MIMS number: | 2007.180 |

Deposited By: | Mrs Louise Healey |

Deposited On: | 20 November 2007 |

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