On Stability of Gorenstein Categories

Author： Xu Aimin   Ding Nanqing  

Publisher： Taylor & Francis Ltd

ISSN： 0092-7872

Source： Communications in Algebra, Vol.41, Iss.10, 2013-10, pp. : 3793-3804

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Abstract

We show that an iteration of the procedure used to define the Gorenstein projective modules over a ring R yields exactly the Gorenstein projective modules. Specifically, given an exact sequence of Gorenstein projective left R-modules G = … → G 1 → G 0 → G 0 → G 1 → … such that the complex Hom R (G, H) is exact for each projective left R-module H, the module Im(G 0 → G 0) is Gorenstein projective. We also get similar results for Gorenstein flat left R-modules when R is a right coherent ring. As applications, we obtain the corresponding results for Gorenstein complexes.

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