Semi-dualizing modules and related Gorenstein homological dimensions
In this paper, the authors define for every semi-dualizing \(A\)-module \(C\), three new Gorenstein dimensions: \(C-\text{Gid}_A(-)\), \(C-\text{Gpd}_A(-)\) and \(C-\text{Gfd}_A(-)\), which are called the \(C\)-Gorenstein injective, \(C\)-Gorenstein projective and \(C\)-Gorenstein flat dimension, respectively, and prove how they are related to the ``change ring'' Gorenstein dimensions over \(A\ltimes C\). Moreover, the authors interpret the \(C\)-Gorenstein dimensions in terms of Auslander and Bass categories and investigate the properties of proper \(C\)-Gorenstein dimensions.
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