Let $R$ be a commutative ring with identity. I'd like to know how to determine the set $\text{Aut}\_R(R[X])$ of all $R$-automorphisms of $R[X]$. 


I've proved that all $\sigma\in\text{Aut}\_R(R[X])$ must satisfy $\sigma(X)=f(X)(X-a)$ (where the constant term of $f$ is invertible and the coefficients of other terms are nilpotent). Thus if $R$ is reduced, $\text{Aut}\_R(R[X])=\{X\mapsto aX+b|\ a\in R^\times,b\in R\}$ ($R^\times$ is the group of units of $R$). How about the general cases?



Structure of $\text{Aut}_R(R[X])$
This is solved by R. Gilmer in his paper *$R$-automorphisms of $R[X]$* appared in the *Proceedings of London Mathematical Society*, (3) 18, pp. 328-33, (1968).


If you want to replace the polynomal ring $R[X]$ by the formal power series $R[[X]]$, look at M. O'Malley and C. Wood's *$R$-endomophisms of $R[[X]]$* in *Journal of Algebra* (15) 314-327 (1970).


