grandes-ecoles 2023 Q1

grandes-ecoles · France · centrale-maths1__official Groups Automorphism and Endomorphism Structure

Let $a \in \mathbb{K}$. For all $p \in \mathbb{K}[X]$, we set $E_a(p) = E_a p = p(X+a)$.
Show that $E_a$ is an automorphism of $\mathbb{K}[X]$.

Let $a \in \mathbb{K}$. For all $p \in \mathbb{K}[X]$, we set $E_a(p) = E_a p = p(X+a)$.

Show that $E_a$ is an automorphism of $\mathbb{K}[X]$.