(Solved): 2. Let :RS be a ring homomorphism. (a) Show that :(R,+)(S,+) is a group homomorphism. (b) ...
2. Let φ:R→S be a ring homomorphism. (a) Show that φ:(R,+)→(S,+) is a group homomorphism. (b) Show that φ×:(R×,×)→(S×,×)is a group homomorphism. Make sure you check that the codomain of φ is indeed S×and not just S. (c) Show that if gcd(m,n)=1, then Znm×≅Zn××Zm×.