Automorphism group of a module

Definition
Let $$R$$ be a (unital) ring and $$M$$ a module over $$R$$. An automorphism of $$M$$ (as a $$R$$-module) is defined as a bijection from $$M$$ to $$M$$ that commutes with the action of each element of $$R$$. The automorphism group of $$M$$ is defined as the group of all automorphisms of $$M$$ as a $$R$$-module. We denote this as $$Aut_R(M)$$.

If $$M$$ is a free module of order $$n$$ over $$R$$, then $$Aut_R(M)$$ can be identified with $$GL(n,R)$$ (by choosing a freely generating set). In particular, this works when $$R$$ is a field or a skew field.