Abstract
Over any associative ring R R it is standard to derive H o m R ( − , − ) \mathrm {Hom}_R(-,-) using projective resolutions in the first variable, or injective resolutions in the second variable, and doing this, one obtains E x t R n ( − , − ) \mathrm {Ext}_R^n(-,-) in both cases. We examine the situation where projective and injective modules are replaced by Gorenstein projective and Gorenstein injective ones, respectively. Furthermore, we derive the tensor product − ⊗ R − -\otimes _R- using Gorenstein flat modules.
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