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?
Follow Math Help Forum on Facebook and Google+
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 $\displaystyle \mathbb{F}_p$.
View Tag Cloud