2. Let :RS be a ring homomorphism. (a) Show that :(R,+)(S,+) is a group homomorphism. (b) Show that :(R,)(S,)is a group homomorphism. Make sure you check that the codomain of is indeed Sand not just S. (c) Show that if gcd(m,n)=1, then ZnmZnZm.

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2. Let :RS be a ring homomorphism. (a) Show that :(R,+)(S,+) is a group homomorphism. (b) Show that :(R,)(S,)is a group homomorphism. Make sure you check that the codomain of  is indeed Sand not just S. (c) Show that if gcd(m,n)=1, then ZnmZnZm.

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(Solved): 2. Let :RS be a ring homomorphism. (a) Show that :(R,+)(S,+) is a group homomorphism. (b) ...

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