# nLab perfect field

A field (in the sense of commutative algebra) $F$ is perfect if every algebraic extension? of $F$ is separable. For example, 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 July 18, 2010 06:51:05 by John Baez (218.186.10.237)