# Field Theory

• Nov 21st 2008, 11:51 PM
whipflip15
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?
• Nov 22nd 2008, 12:30 AM
NonCommAlg
Quote:

Originally Posted by whipflip15

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 $\mathbb{F}_p[x].$
• Nov 22nd 2008, 02:33 PM
ThePerfectHacker
Quote:

Originally Posted by whipflip15
Anyway, is it possible to have infinite field with characteristic not 0?

Construct $\bar {\mathbb{F}_p}$ to be the algebraic closure for $\mathbb{F}_p$.