# Rings and Fields- how to prove Z[x]/pZ[x] is an integral domain

1. Feb 27, 2013

1. The problem statement, all variables and given/known data

Prove Z[x]/pZ[x] is an integral domain where p is a prime natural number.

2. Relevant equations

I've seen in notes that this quotient ring can be isomorphic to (z/p)[x] and this is an integral domain but I don't know how to prove there is an isomorphism between them and how to prove it is an integral domain...

3. The attempt at a solution

2. Feb 27, 2013

### micromass

Staff Emeritus
Do you have any suggestion about what the isomorphism will be?? Just write down some map that looks intuitively right, most of the time this works.