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Paper   IPM / M / 8611
School of Mathematics
  Title:   Stability of Gorenstein categories
  Author(s):  T. Sharif (Joint with S. Sather-Wagstaff and D. White)
  Status:   Published
  Journal: J. London Math. Soc.
  Vol.:  77
  Year:  2008
  Pages:   481-502
  Supported by:  IPM
We show that an iteration of the procedure used to define the Gorenstein projective modules over a commutative ring R yields exactly the Gorenstein projective modules. Specifically, given an exact sequence of Gorenstein projective R-modules G=...\xra∂G2G1\xra∂G1G0\xra∂G0 ... such that the complexes \HomR(G,H) and \HomR(H,G) are exact for each Gorenstein projective R-module H, the module \coker(∂G1) is Gorenstein projective. The proof of this result hinges upon our analysis of Gorenstein subcategories of abelian categories.

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