The orthogonal complement relative to the functor extension of the class of all Gorenstein projective modules (Q421898)

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scientific article; zbMATH DE number 6035370
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The orthogonal complement relative to the functor extension of the class of all Gorenstein projective modules
scientific article; zbMATH DE number 6035370

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    The orthogonal complement relative to the functor extension of the class of all Gorenstein projective modules (English)
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    15 May 2012
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    For a ring \(R\), let \(\mathcal{G}P\) be the class of Gorenstein projective left \(R\)-modules, and \(\mathcal{G}P^{\perp}\) be the class of all modules \(M\) such that \(\text{Ext}^1_R(X,M)=0\) for every \(X\in \mathcal{G}P\). The author shows that if the left Gorenstein global dimension of \(R\) is finite, then \((\mathcal{G}P,\mathcal{G}P^{\perp})\) is a complete hereditary cotorsion pair.
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    cotorsion theory
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    Gorenstein homological dimensions of modules and rings
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