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|Paper IPM / M / 8611||
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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