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Homework Help: Show isomorphism

  1. Oct 17, 2013 #1
    1. The problem statement, all variables and given/known data

    Show that for any rings R and S, R x S and S x R are isomorphic, and A x B is the cartesian product, or ordered pairs. So an element of R x S can be written as (r1, s1).

    2. Relevant equations

    3. The attempt at a solution

    So I have to show that there is a bijection from R x S to S x R, and this bijection must preserve addition and multiplication. This is tough for me since the mapping from R x S to S x R could be anything! How can I even start if I don't have this function or mapping?
  2. jcsd
  3. Oct 17, 2013 #2


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    Science Advisor
    Homework Helper

    hi stripes! :smile:
    yes it could

    but you're in charge, and you can choose any mapping you like :smile:

    go for the "natural" mapping …

    what do you think it would be really neat for (r1, s1) to be mapped onto? :wink:
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