Let R be a commutative ring.
It is well known that the automorphism group of the module $R^n$ is isomorphic to $GL_n(R)$. Is their a way to measure how much this fails for an arbitrary module M? Perhaps some short exact sequence involving $GL_n(R)$ and $Aut(M)$.
It feels like a natural question. I can imagine this failing without any conditions on M or R. But perhaps one of you knows something about this.