Quadratic 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
A field extension is termed a quadratic extension if it satisfies the following equivalent conditions:
- It is the splitting field for an irreducible polynomial of degree two.
- It is a extension of degree two.
- It is a normal extension of degree two.
Relation with other properties
Weaker properties
- Finite normal extension
- Finite extension
- Normal extension: For full proof, refer: Quadratic implies normal