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#1

$Old$ November 22nd, 2008, 12:51 AM

whipflip15 $whipflip15 is offline$

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$Default$ 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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$Old$ November 22nd, 2008, 01:30 AM

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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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$Old$ November 22nd, 2008, 03:33 PM

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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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