View source for Formally real field

{{TEX|done}}{{MSC|12J15}}

A field $F$ which is capable of being made an [[ordered field]].  The existence of such an order is equivalent to the property that $-1$ is not a sum of squares in $F$: this is the Artin--Schreier theorem.  A [[real closed field]] is a formally real field for which no algebraic extension is formally real.

====References====
* Tsit Yuen Lam, ''Introduction to Quadratic Forms over Fields'',  Graduate Studies in Mathematics '''67''',  American Mathematical Society (2005) {{ISBN|0-8218-1095-2}} {{ZBL|1068.11023}} {{MR|2104929 }}
* A. R. Rajwade, ''Squares'', London Mathematical Society Lecture Note Series '''171''' Cambridge University Press (1993) {{ISBN|0-521-42668-5}} {{ZBL|0785.11022}}
* J.W. Milnor, D. Husemöller, ''Symmetric bilinear forms'', Ergebnisse der Mathematik und ihrer Grenzgebiete '''73''', Springer-Verlag (1973) {{ISBN|0-387-06009-X}} {{ZBL|0292.10016}}