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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Gorenstein derived functors


Author: Henrik Holm
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1913-1923
MSC (2000): Primary 13D02, 13D05, 13D07, 13H10, 16E05, 16E10, 16E30
Published electronically: February 13, 2004
MathSciNet review: 2053961
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Abstract: Over any associative ring $R$ it is standard to derive $\mathrm{Hom}_R(-,-)$using projective resolutions in the first variable, or injective resolutions in the second variable, and doing this, one obtains $\mathrm{Ext}_R^n(-,-)$ in both cases. We examine the situation where projective and injective modules are replaced by Gorenstein projective and Gorenstein injective ones, respectively. Furthermore, we derive the tensor product $-\otimes_R-$ using Gorenstein flat modules.


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Additional Information

Henrik Holm
Affiliation: Matematisk Afdeling, Københavns Universitet, Universitetsparken 5, 2100 K\obenhavnØ, DK–Danmark
Email: holm@math.ku.dk

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07317-4
PII: S 0002-9939(04)07317-4
Keywords: Gorenstein dimensions, homological dimensions, derived functors, Tor-modules, Ext-modules
Received by editor(s): May 14, 2002
Received by editor(s) in revised form: April 16, 2003
Published electronically: February 13, 2004
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2004 American Mathematical Society