The Properties Of Gorenstein C-homological Modules

In this paper, we mainly study the properties of Gorenstein homo-logical modules (that is, Gorenstein C-projective modules, Gorenstein C-injective modules and Gorenstein C-fiat modules) with respect to a semidu-alizing module C. First of all, we introduce the notions of two-degree Goren-stein C-homological modules, and investigate the stability of Gorenstein C-homological modules. It is show that the class of Gorenstein C-homological modules has a strong stability. Then, we consider properties of Gorenstein C-homological modules and dimensions under change of rings.