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Math Help - Field Theory

  1. #1
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    Field Theory

    It is a well known that every polynomial over a field of characteristic zero is separable. We also know that every polynomial over a finite field is separable.

    Anyway, is it possible to have infinite field with characteristic not 0?
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  2. #2
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    Quote Originally Posted by whipflip15 View Post

    Anyway, is it possible to have infinite field with characteristic not 0?
    of course it's possible! for example \mathbb{F}_p(x), the field of fractions of \mathbb{F}_p[x].
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    Quote Originally Posted by whipflip15 View Post
    Anyway, is it possible to have infinite field with characteristic not 0?
    Construct \bar {\mathbb{F}_p} to be the algebraic closure for \mathbb{F}_p.
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