  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
$R \rightarrow M$. 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.
