#
nLab

field extension

# Contents

## Idea

If a subset $k$ of a field $K$ is a subfield, then we call the larger field $K$ an **extension** of the smaller field $k$.

More generally, if $k \to K$ is *any* ring homomorphism between fields, then it must be an injection, so we may treat it as a field extension.

Revised on December 9, 2013 05:53:49
by

Urs Schreiber
(89.204.139.250)