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Math Help - Commutative Ring

  1. #1
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    Commutative Ring

    My professor gave us this query at the end of class, and I started thinking about axioms, but I didn't think of anything that would have to make the following statement true. Thoughts?

    What must be true about a nontrivial commutative ring R in order to conclude
    (a+b)^4 = a^4 + 2a^2b^2 + b^4 for all elements a and b in R?

    Clarification would be great on this one.
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  2. #2
    Senior Member roninpro's Avatar
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    Note that by the binomial theorem,

    (a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4

    If the ring has characteristic 4, that is, 4x=0 for all x\in R, then this would simplify to

    a^4+2a^2b^2+b^4
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  3. #3
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    So that just means it has to be characteristic 4?
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