Gorenstein FP-injective and Gorenstein flat modules

摘要

In this paper, Gorenstein FP-injective modules are introduced and studied. An R-module M is called Gorenstein FP-injective if there is an exact sequence ... -> E-1 -> E-0 -> E-0 -> E-1 -> ... of injective R-modules with M = ker(E-0 -> E-1) and such that Hom(E,-) leaves the sequence exact whenever E is an FP-injective R-module. Some properties of Gorenstein FP-injective and Gorenstein flat modules over coherent rings are obtained. Several known results are extended.