Frobenius endomorphism
= Frobenius endomorphism
{c}
{title2=$x\mapsto x^p$}
{wiki}
In a field of characteristic $p>0$, the Frobenius map $x\mapsto x^p$ is an injective field endomorphism because
$$
(x+y)^p=x^p+y^p.
$$
Consequently every element of an extension field has at most one $p$th root.