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## Homework Statement

Prove that [tex]\phi[/tex] : Z

_{p}[tex]\rightarrow[/tex] Z

_{p},

[tex]\phi[/tex] (a) = a

^{p}is a ring homomorphism, find the ker [tex]\phi[/tex]

## Homework Equations

## The Attempt at a Solution

So show that a [tex]_{p}[/tex] + b [tex]_{p}[/tex] = (a + b)

^{p}?

and (ab)

^{p}= (a

^{p})(b

^{p})?

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