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Stability of Gorenstein categories
Author(s) -
Sather-Wagstaff Keri Ann,
Sharif Tirdad,
White Diana
Publication year - 2008
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm124
Subject(s) - mathematics , pure mathematics , exact sequence , projective test , commutative property , commutative ring , sequence (biology) , abelian group , projective cover , discrete mathematics , collineation , projective space , genetics , biology
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 ‐modulesG = ⋯ → ∂ 2 GG 1 → ∂ 1 GG 0 → ∂ 0 G⋯such that the complexes Hom R ( G, H ) and Hom R ( H, G ) are exact for each Gorenstein projective R ‐module H , the module Coker ( ∂ 1 G ) is Gorenstein projective. The proof of this result hinges upon our analysis of Gorenstein subcategories of abelian categories.