Prime Ideals gotten from homomorphisms I am asked to prove that every prime ideal P of a ring R can be obtained as the kernel of a homomorphism to a field. 
I know that the kernel of a homomorphism is an ideal. I need to start from an arbitrary prime ideal and show that it is the kernel of a homomorphism. So it would seem that this would not help, since it would be proving something (that it is an ideal) that I am already assuming (the prime ideal). 
Could someone please give ideals how to prove this?

Hints:
The projection $R\to R/P$ is a homomorphism of $R$ to a domain, and this map's kernel is $P$.
Integral domains embed in their field of fractions.
Can you take it from here?
