IFP Injective Dimensions And Gorenstein IFP-injective Modules

IFP-injective modules,as a generalization of injective modules,forms a class closed under direct limits.In this paper,we investigate the IFP-injective dimensions of modules.For example,u’D(R)= l.IFP-dim(R)= gl right IJ-dim(RM);the relation between IFP-injective dimension and the nth Ext group are shown.When R is a left semi-hereditary ring,the existence of IFP-injective preenvelope are stated.When R is a left coherent ring,equivalent conditions of Gorenstein IFP-injective modules are given;R is a left Noetherian ring if and only if ev-ery IFP-injective module is Gorenstein IFP-injective.When R is a n-FC ring,every Gorenstein IFP-injective module is IFP-injective.When R is a n-FC ring and perfect ring,every R-module has a Gorenstein IFP-injective preenvelope;(Pn,G-IJ)is a perfect cotorsion theory;every pure-injective R-module has a Gorenstein IFP-injective precover.