Looking for help on the following problem:
Let R, a ring be Z[x] (polynomials with integer coefficients). Let (2,x) be the ideal generated by 2 and x.
1.) Prove that the ideal (2,x) is not principal and conclude that Z[x] is not a principal ideal ring.
2.) Find a homomorphism f: R to Z2 such that (2,x)=Ker(f).