# Tower of fields

In mathematics, a tower of fields is a sequence of field extensions

F0F1 ⊆ ... ⊆ Fn ⊆ ...

The name comes from such sequences often being written in the form

$\begin{array}{c}\vdots \\ | \\ F_2 \\ | \\ F_1 \\ | \\F_0. \end{array}$

A tower of fields may be finite or infinite.

## Examples

• QRC is a finite tower with rational, real and complex numbers.
• The sequence obtained by letting F0 be the rational numbers Q, and letting
$F_{n+1}=F_n\left(2^{1/2^n}\right)$
(i.e. Fn+1 is obtained from Fn by adjoining a 2nth root of 2) is an infinite tower.