nLab
perfect field

Contents

Definition

A field (in the sense of commutative algebra) FF is perfect if every algebraic extension of FF 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)