Stability of Gorenstein categories

• Autores: Sean Sather-Wagstaff, Tirdad Sharif, Diana White
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 77, Nº 2, 2008, págs. 481-502
• Idioma: inglés
• DOI: 10.1112/jlms/jdm124
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• Resumen

  • 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 such that the complexes HomR(G, H) and HomR(H, G) are exact for each Gorenstein projective R-module H, the module Coker() is Gorenstein projective. The proof of this result hinges upon our analysis of Gorenstein subcategories of abelian categories.