Definition:Frobenius Endomorphism

Definition
Let $p$ be a prime number.

Let $R$ be a commutative ring with unity of characteristic $p$.

The Frobenius endomorphism is the ring endomorphism $\operatorname{Frob} : R\to R$ defined as:
 * $\operatorname{Frob} : x \mapsto x^p$

Also see

 * Frobenius Endomorphism on Field is Injective
 * Frobenius Endomorphism is Endomorphism
 * Definition:Perfect Field