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Math Help - Ring-Homomorphisms

  1. #1
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    Ring-Homomorphisms

    Find all ring-homomorphisms \Phi: Z_n \rightarrow Z_m

    Thanks!
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  2. #2
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    Quote Originally Posted by roporte View Post
    Find all ring-homomorphisms \Phi: Z_n \rightarrow Z_m
    First, [1]_n\mapsto [1]_m by definition - (by definition for ring homomorphism for commutative rings).

    A ring homomorphism is also a group homomorphism between (\mathbb{Z}_n,+) and (\mathbb{Z}_m,+). Since [1]_n generates the group it means this homomorphism is completely determined by its value on this element. Can you finish it now?
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