\begin{definition}[Definition:Frobenius Endomorphism]
Let $p$ be a prime number.
Let $R$ be a commutative ring with unity of characteristic $p$.
The '''Frobenius endomorphism''' is the ring endomorphism $\Frob: R \to R$ defined as:
:$\forall x \in R: \map \Frob x = x^p$
\end{definition}