A module over a unit ring 
is called divisible if, for all 
which are not zero divisors, every
element 
of 
can be "divided" by 
, in the sense that there is an element 
in 
such that 
. This condition can be reformulated by saying that the
multiplication by 
defines a surjective map from 
to 
.
It can be shown that every injective 
-module is divisible, but the converse only holds for particular
classes of rings, e.g., for principal ideal domains. Since 
and 
are evidently divisible 
-modules, this allows us to conclude that they are also injective.
An additive Abelian group is called divisible if it is so as a 
-module.
