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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Gorenstein projective dimension for complexes
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by Oana Veliche PDF
Trans. Amer. Math. Soc. 358 (2006), 1257-1283 Request permission

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
  • Received by editor(s): October 8, 2003
  • Received by editor(s) in revised form: May 8, 2004
  • Published electronically: May 26, 2005
  • © Copyright 2005 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 358 (2006), 1257-1283
  • MSC (2000): Primary 16E10, 18G25, 13D05; Secondary 13D25, 16E30, 16E45
  • DOI: https://doi.org/10.1090/S0002-9947-05-03771-2
  • MathSciNet review: 2187653