Algebraic 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

Symbol-free definition

A field extension is termed algebraic if it satisfies the following equivalent conditions:

1. Every element in the extension is algebraic over the base field.
2. The sub-extension generated by any finite subset of the extension is a finite extension of the base field.

Relation with other properties

Stronger properties

• Galois extension
• Normal extension
• Finite extension