On Stability of Gorenstein Categories |
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Authors: | Aimin Xu |
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Affiliation: | Department of Mathematics , Nanjing University , Nanjing , China |
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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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Keywords: | Gorenstein flat complex Gorenstein projective complex Self-orthogonal class 𝒲 -Gorenstein module |
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