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

A tower of fields may be finite or infinite.


  • QRC is a finite tower with rational, real and complex numbers.
  • The sequence obtained by letting F0 be the rational numbers Q, and letting
(i.e. Fn+1 is obtained from Fn by adjoining a 2nth root of 2) is an infinite tower.


  • Section 4.1.4 of Escofier, Jean-Pierre (2001), Galois theory, Graduate Texts in Mathematics, 204, Springer-Verlag, ISBN 978-0-387-98765-1
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