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Calculating the characteristic of the cartesian product of rings

  1. Oct 16, 2013 #1
    1. The problem statement, all variables and given/known data

    See attached image
    attachment.php?attachmentid=63020&stc=1&d=1381953319.jpg

    2. Relevant equations



    3. The attempt at a solution

    For the first half of the question, ordered pairs would be (1, [1]), since 1 and [1] are the multiplicative identities in these rings. but no matter how many times we add (1, [1]) to itself, we'll never get (1, [1]) again. does this mean this ring has zero characteristic?
     

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    Last edited: Oct 16, 2013
  2. jcsd
  3. Oct 16, 2013 #2

    Dick

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    Yes, it has zero characteristic. What about the other ring?
     
  4. Oct 17, 2013 #3
    Other ring has characteristic 12, I hope.
     
  5. Oct 17, 2013 #4

    Dick

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    Sure it is, it's the least common multiple of 4 and 6.
     
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