Gorenstein S-Injective Modules And Dimension

In the first chapter,backgrounds and preliminaries are given.In the second chap-ter,the definition of strongly FP_?modules is introduced,modules in the right orthogo-nal class?resp.,left orthogonal class?of the class of strongly FP_?modules respects to functors Ext_R¹?-,-?and Tor₁^R?-,-?,which we call S-injective and S-flat modules are investigated.Then some properties of S-injective are given,that is Especially,it is proved that an R-module M is S-injective if and only if M+ is S-flat.In the third chapter,the definition of Gorenstein S-injective modules is introduced,some equivalent characteriza-tions of Gorenstein S-injective modules are given.Especially,it is proved that the class of Gorenstein S-injective R-modules is injectively resolving.Finally,some equivalent characterizations of Gorenstein S-injective dimensions of an R-module M are given.