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Triangulated Equivalences Involving Gorenstein Projective Modules
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- Journal:
- Canadian Mathematical Bulletin / Volume 60 / Issue 4 / 01 December 2017
- Published online by Cambridge University Press:
- 20 November 2018, pp. 879-890
- Print publication:
- 01 December 2017
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- Article
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For any ring
$R$, we show that, in the bounded derived category 
${{D}^{b}}(\text{Mod}\,R)$ of left $R$-modules, the subcategory of complexes with finite Gorenstein projective (resp. injective) dimension modulo the subcategory of complexes with finite projective (resp. injective) dimension is equivalent to the stable category 
$\underline{\text{GP}}(\text{Mod}\,R)\,(resp.\overline{GI}(Mod\,R))$ of Gorenstein projective (resp. injective) modules. As a consequence, we get that if $R$ is a left and right noetherian ring admitting a dualizing complex, then 
$\underline{\text{GP}}(\text{Mod}\,R)$ and 
$\overline{\text{GI}}(\text{Mod}\,R)$ are equivalent.
