Stability of Gorenstein Categories
Abstract
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=...∂G2G1∂G1G0∂G0 ... such that the complexes R(G,H) and R(H,G) are exact for each Gorenstein projective R-module H, the module (∂G1) is Gorenstein projective. The proof of this result hinges upon our analysis of Gorenstein subcategories of abelian categories.
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