Definition:Identity Automorphism

Definition
Let $\left({R, +, \circ}\right)$ be a ring.

Consider the identity mapping $I_R: R \to R$:
 * $\forall r \in R: I_R \left({r}\right) = r$

Then $I_R$ is the identity automorphism on $R$.

Also see
In Identity Mapping is Ring Automorphism it is demonstrated that $I_R$ is indeed a (ring) automorphism.