In mathematics, a sequence of field extensions
In mathematics, a tower of fields is a sequence of field extensions
- F0 ⊆ F1 ⊆ ... ⊆ Fn ⊆ ...
The name comes from such sequences often being written in the form
A tower of fields may be finite or infinite.
Examples
- Q ⊆ R ⊆ C 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 is obtained from Fn-1 by adjoining a 2n th root of 2), is an infinite tower.
References