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Find ALL of the homomorphisms?

  1. Nov 22, 2004 #1
    I'm trying to figure out all of the homomorphisms from Z onto Z mod 12. I can't figure out the trick - how am I possibly going to find ALL of the homomorphisms?

    Thanks -
  2. jcsd
  3. Nov 23, 2004 #2

    matt grime

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    A homomorphism of Z to anything is explicitly determined by its kernel and where 1 goes to. This is now enough (I hope) information to solve the problem once you say if you mean as an additive group or as a ring.
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