Homological Properties Of Modules Under Base Changes

In this paper,we first define a flat bimodule with the property of flat ring extensions.Under this definition,we consider the homological property of Gorenstein modules under flat bimodules,which generalizes some results of homological property of Gorenstein modules under flat ring extensions over commutative rings.Secondly,we study the relations between Auslander classes and Bass classes under flat bimodules whenever there is a semi-dualing module,and study Gorenstein properties with respect to flat bimodules.Finally,we give the nation of define faithful flat bimodules and consider the cobase changes of weak Gorenstein injective modules.