# Extension (mathematics)

In

mathematics , the word**"extension"**has many uses. See:**Analysis***

Carathéodory's extension theorem

*Continuous linear extension

*M. Riesz extension theorem

*Krein extension theorem

*Hahn-Banach theorem **Algebra***

Abelian extension

*Algebraic extension

*Artin-Schreier extension

* Central extension

* Cyclotomic extension—seeabelian extension

*Degree of a field extension

*Dual basis in a field extension

*Extension problem

*Field extension

*Galois extension

*Group extension

*Integral extension

*Kernel extension theorem

*Kummer extension

*Normal extension

*Quadratic extension

*Quadratic field extension

*Ring extension

*Separable extension

*Simple extension

*Splitting of prime ideals in Galois extensions

* Trivial extension—seefield extension **Algebraic geometry***

Sheaf extension **Logic / Set theory***

Axiom of extensionality

*Extensible cardinal

*Extension (model theory)

*Extension (predicate logic)

*Extensionality **Order theory***

Linear extension **Probability theory***

Kolmogorov extension theorem **Topology***

Homotopy extension property

*Tietze extension theorem **Geometry***

Exterior algebra , Grassmann's "theory of extension".

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