nLab
formally real field

Formally real fields

Formally real fields

Definition

A field kk is formally real if one of the following equivalent conditions is satisfied:

Due to the last property, formally real fields play a special rôle in the theory of Witt groups? and in related fields of study such as motivic homotopy theory.

A formally real field which is the only formally real algebraic extension of itself is a real closed field; such a field admits a unique ordering (not requiring Zorn's Lemma).

Examples

category: algebra

Last revised on August 15, 2020 at 04:55:12. See the history of this page for a list of all contributions to it.