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Math Help - (X^4)+(4x^2)+144

  1. #1
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    Dec 2010
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    (X^4)+(4x^2)+144

    for the following equation in the title, can anyone help us to find out the following information:
    1) how can this equation be used to contruct a field?
    2)how does this connect with algerbraic elements?
    3) with maximal ideals?
    4)with contructable real numbers?
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  2. #2
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    Quote Originally Posted by vpatel View Post
    for the following equation in the title, can anyone help us to find out the following information:
    1) how can this equation be used to contruct a field?
    2)how does this connect with algerbraic elements?
    3) with maximal ideals?
    4)with contructable real numbers?

    For example, find a prime finite field \mathbb{F}_p:=\mathbb{Z}/p\mathbb{Z} where this pol. is irreducible , and

    then the ideal M:=\langle x^4+4x^2+144\rangle is maximal in \mathbb{F}_p[x]\Longrightarrow \mathbb{F}_p[x]/M is a field (with p^4 elements)...

    Of course, you can try the above also with some field \mathbb{F} with characteristic zero...

    Tonio
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