# Thread: Units in a polynomial ring

1. ## Units in a polynomial ring

Challenge question:

Let $R$ be a commutative ring and $f(x)=a_0+...+a_nx^n \in R[x]$ then $f$ is a unit if and only if $a_0$ is a unit and $a_1,...a_n$ are nilpotent.

I have a solution using more involved ring theory, but I'm really interested to see more elementary solutions (or even more involved or indirect, why not).

Moderator approved CB

2. see my post in here.