# 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 $\Frob: R \to R$ defined as:

$\forall x \in R: \map \Frob x = x^p$

## Source of Name

This entry was named for Ferdinand Georg Frobenius.