# Contents

## Definition

A field (in the sense of commutative algebra) $F$ is perfect if every algebraic extension of $F$ is separable.

## Examples

All fields of characteristic zero are perfect, as are all finite fields, and all algebraically closed fields, and all extensions of perfect fields.

An example of a field that isn’t perfect is the field of rational functions over a finite field.

Revised on November 18, 2013 05:38:49 by Urs Schreiber (89.204.130.234)