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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Gorenstein projective dimension for complexes


Author: Oana Veliche
Journal: Trans. Amer. Math. Soc. 358 (2006), 1257-1283
MSC (2000): Primary 16E10, 18G25, 13D05; Secondary 13D25, 16E30, 16E45
Published electronically: May 26, 2005
MathSciNet review: 2187653
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Abstract: We define and study a notion of Gorenstein projective dimension for complexes of left modules over associative rings. For complexes of finite Gorenstein projective dimension we define and study a Tate cohomology theory. Tate cohomology groups have a natural transformation to classical Ext groups. In the case of module arguments, we show that these maps fit into a long exact sequence, where every third term is a relative cohomology group defined for left modules of finite Gorenstein projective dimension.


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Additional Information

Oana Veliche
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: oveliche@math.purdue.edu, oveliche@math.utah.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03771-2
PII: S 0002-9947(05)03771-2
Received by editor(s): October 8, 2003
Received by editor(s) in revised form: May 8, 2004
Published electronically: May 26, 2005
Article copyright: © Copyright 2005 American Mathematical Society