Thread: 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?

Originally Posted by whipflip15

Anyway, is it possible to have infinite field with characteristic not 0?

of course it's possible! for example $\displaystyle \mathbb{F}_p(x),$ the field of fractions of $\displaystyle \mathbb{F}_p[x].$

Originally Posted by whipflip15

Anyway, is it possible to have infinite field with characteristic not 0?

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