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.
