# Ring homomorphism

## Homework Statement

Prove that $$\phi$$ : Zp $$\rightarrow$$ Zp,
$$\phi$$ (a) = a p is a ring homomorphism, find the ker $$\phi$$

## The Attempt at a Solution

So show that a $$_{p}$$ + b $$_{p}$$ = (a + b)p?
and (ab)p = (ap)(bp)?

Last edited:

Dick
Homework Helper
Yes, show those equalities mod p. The second is easy. For the first think about the binomial theorem. Is p supposed to be a prime?

p is prime.
so show a mod p + b mod p = (a+b) mod p
and (ab) mod p = (a mod p)*(b mod p)
how do i do that?

Dick