Rings without a Gorenstein analogue of the Govorov-Lazard Theorem

Details Rings without a Gorenstein analogue of the Govorov-Lazard Theorem Rings without a Gorenstein analogue of the Govorov-Lazard Theorem

2008-10-17

arxiv.org/abs/0810.3168v2

Mathematics

Commutative Algebra

15 pages. References added and title changed

Scientific paper

It 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.

Affiliated with

Also associated with

No associations

Rating

Rings without a Gorenstein analogue of the Govorov-Lazard Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Rings without a Gorenstein analogue of the Govorov-Lazard Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rings without a Gorenstein analogue of the Govorov-Lazard Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-352571