Finite 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

Definition with symbols

Suppose $L$ is a field extension of a field $K$ (i.e., $K$ is a subfield of $L$). We say that $L$ is a finite extension of $K$ if the degree of the extension, denoted $[L:K]$, is finite, where the degree is defined as the dimension of $L$ as a $K$-vector space.