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Thread: Need helpful hints

  1. #1
    Junior Member
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    Need helpful hints

    Hey everyone. If anyone could point me towards a hint on the following problem I would greatly appreciate it.

    Let n and m be positive integers, with n > m ≥ 2. Describe as completely as you can the possible ring homomorphisms from Zn to Zm. Under what conditions on n and n will there be nontrivial homomorphisms? Under what conditions on n and m will there be surjective homomorphisms?
    Last edited by HeirToPendragon; Dec 9th 2009 at 06:53 AM.
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  2. #2
    MHF Contributor

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    Start by looking at a couple of simple examples. What are the possible homomorphisms from $\displaystyle Z_3$ to $\displaystyle Z_2$? What about $\displaystyle Z_4$ to $\displaystyle Z_2$? What about $\displaystyle Z_6$ to $\displaystyle Z_2$ or $\displaystyle Z_3$?
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