Tower of fields

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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[edit]

  • 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.

References[edit]