Thread: Ring Homomorphisms

Determine all ring homomorphisms of into .

Clearly justify your method.

Since every element in ZxZ can be written as m(1,0) + n(0,1) for m,n in I think every homomorphism would send [ (1,0) to (n,0), (0,1) to (0,m) ]for integers n, m and then theres just the identity homomorphism.