Rings without a Gorenstein analogue of the Govorov-Lazard Theorem

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dc.creatorHolm, Henrik
dc.creatorJorgensen, Peter
dc.date2008-10-17
dc.date2008-11-10
dc.date.accessioned2026-07-07T10:16:47Z
dc.date.available2026-07-07T10:16:47Z
dc.descriptionIt was proved by Beligiannis and Krause that over certain Artin algebras, there are Gorenstein flat modules which are not direct limits of finitely generated Gorenstein projective modules. That is, these algebras have no Gorenstein analogue of the Govorov-Lazard Theorem. We show that, in fact, there is a large class of rings without such an analogue. Namely, let R be a commutative local noetherian ring. Then the analogue fails for R if it has a dualizing complex, is henselian, not Gorenstein, and has a finitely generated Gorenstein projective module which is not free. The proof is based on a theory of Gorenstein projective (pre)envelopes. We show, among other things, that the finitely generated Gorenstein projective modules form an enveloping class in mod R if and only if R is Gorenstein or has the property that each finitely generated Gorenstein projective module is free. This is analogous to a recent result on covers by Christensen, Piepmeyer, Striuli, and Takahashi, and their methods are an important input to our work.
dc.description15 pages. References added and title changed
dc.identifierhttps://arxiv.org/abs/0810.3168
dc.identifierhttp://arxiv.org/abs/0810.3168
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173628
dc.subjectCommutative Algebra
dc.subjectK-Theory and Homology
dc.subject13H10, 18G25
dc.titleRings without a Gorenstein analogue of the Govorov-Lazard Theorem
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