Galois extension

This article defines a field extension property: a property that can be evaluated to true/false for any field extension.
View a complete list of field extension properties|View a complete list of field properties

Definition

Suppose $L$ is a field extension of a field $K$. In other words, $K$ is a subfield of $L$. Then, $L$ is termed a Galois extension if $L$ is an algebraic extension of $K$ that is both normal and separable.

Relation with other properties

Stronger properties

• Finite Galois extension

Weaker properties

• Normal extension
• Separable extension
• Algebraic extension