I just need confirmation. I have a problem in my algebra class that says: Prove that there are no ring homomorphisms from Z5 to Z7. I have the following definition of ring homomorphism: Let R and S be rings. A function R to S is a ring homomorphism if the following holds: f(1R)=1S. f(r1+r2)=f(r1)+f(r2) for all r1 and r2 in R. f(r1r2)=f(r1)f(r2) for all r1 and r2 in R. I've been thinking and wouldn't f(x)=0 work? This is a problem in a published textbook so it doesn't make sense to me. Could anyone clue me in to where there might be a contradiction in the definition? Thanks in anticipation. Mike.