Fp-injective Module and its Localization

Abstract

FP-injective modules act in ways similar to injective modules. Therefore, through-out this document we investigate many of these properties of FP-injective modules which are modelled after those similar properties of injective modules. The results we develop can be broken into two categories: FP-injective Modules and Localization of FP-injective Modules. We form S −1M, an S −1R-module, for any R-module M. We state and prove some known results about localizations. Using these known techniques and properties of localizations, we arrive at conditions on the ring R which make an FP-injective S −1R-module into an FP-injective R-module. We then show that under certain conditions, if E is an FP-injective R-module, then S −1E will be an FP-injective S −1R-module.