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Math Help - Infinite Field With Characteristic 5?

  1. #1
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    Infinite Field With Characteristic 5?

    One of my study guide questions says to give an example of such a field. I'm sure there's more than one example. From there, how would I show it has said characteristic?
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  2. #2
    Member Black's Avatar
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    \mathbb{Z}_5(x)=\{f(x)/g(x)|\, f(x),g(x) \in \mathbb{Z}_5[x], \, g(x) \not= 0\} is one, since unity 1 has order 5 under addition.
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