The Stacks project

Remark 111.29.4. Let $h \in {\mathbf Z}[y]$ be a monic polynomial of degree $d$. Then:

1. The map $A = {\mathbf Z}[x] \to B ={\mathbf Z}[y]$, $x \mapsto h$ is finite locally free of rank $d$.

2. For all primes $p$ the map $A_ p = {\mathbf F}_ p[x]\to B_ p = {\mathbf F}_ p[y]$, $y \mapsto h(y) \bmod p$ is finite locally free of rank $d$.