On R-Coneat Injective Modules and Generalizations

Both the classes of R-coneat injective modules and its superclass, pure Baer injective modules, are shown to be preenveloping. The former class is contained in another one, namely, self coneat injectives, i.e. modules M for which every map f from a coneat left ideal of R into M, whose kernel contains the annihilator of some element in M, is induced by a homomorphism R → M. Certain types of rings are characterized by properties of the above modules. For instance, a commutative ring R is von Neuman regular if and only if all self coneat injective R-modules are quasi injective.