In mathematics, the word "extension" enjoys many uses. See:

Exterior algebra, Grassmann's theory of extension.

Splitting of prime ideals in Galois extensions

Trivial extension—see field extension

Degree of a field extension

Extension problem

Hahn-Banach theorem

Carathéodory's extension theorem

Axiom of extensionality

Group extension

Kummer extension

Quadratic extension

Quadratic field extension

Continuous linear extension

Simple extension

Algebraic extension

Separable extension

Kernel extension theorem

Normal extension

Artin-Schreier extension

Cyclotomic extension—see abelian extension

Kolmogorov extension theorem

Dual basis in a field extension

M. Riesz extension theorem

Krein extension theorem

Galois extension

Homotopy extension property

In mathematics, extensionality usually refers to some form of the principle, going back to Leibniz, that two mathematical objects are equal if there is no test to distinguish them. For example, given two mathematical functions f and g, we can say that...

Linear extension

Extension (predicate logic)

Tietze extension theorem

Extension (model theory)

Ring extension

Central extension