FR-Injective Modules Over Coherent Domains

In this paper, an R-module M is called FR-injective if Ext(R)(1)(F,M)=0 for every finitely generated reflexive R-module F. We generalize some properties of FP-injective modules to FR-injective modules, consider the relationships between injective modules, FP-injective modules and FR-injective modules, gives some characterizations of (Pi-coherent) rings with property that all finitely generated reflexive modules are projective, and show that a coherent domain is a Prufer domain if and only if it is an 1-FC domain with finite weak global dimension, a coherent domain R is of w.gl.dim(R)<= 2 if and only if every (finitely generated) ideal of R is FR-injective, and a noetherian domain is 2-Gorenstein if and only if R is self FR-injective. Finally, we discuss some properties of I-FR-covers and I-FR-envelopes, where I-FR denotes the class of all FR-injective modules.