简介：TheauthorsintroduceandinvestigatetheT_C-Gorensteinprojective,L_CGorensteininjectiveandH_C-GorensteinflatmoduleswithrespecttoasemidualizingmoduleCwhichsharesthecommonpropertieswiththeGorensteinprojective,injectiveandflatmodules,respectively.TheauthorsprovethattheclassesofalltheT_C-GorensteinprojectiveortheH_C-GorensteinflatmodulesaxeexactlythoseGorensteinprojectiveorfiatmoduleswhichareintheAuslanderclasswithrespecttoC,respectively,andtheclassesofalltheL_C-GorensteininjectivemodulesaxeexactlythoseGorensteininjectivemoduleswhichareintheBassclass,sotheauthorsgettherelationsbetweentheGorensteinprojective,injectiveorflatmodulesandtheC-Gorensteinprojective,injectiveorflatmodules.Moreover,theauthorsconsidertheT_C(R)-projectiveandL_C(R)-injectivedimensionsandT_C(R)-precoversandL_C(R)-preenvelopes.Finally,theauthorsstudytheH_C-GorensteinflatmodulesandextendtheFoxbyequivalences.