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Formally real field
In mathematics, a formally real field in field theory is a field that shares certain algebraic properties with the real number field. A formally real field F may be characterized in any of the following equivalent ways:
- −1 is not a sum of squares in F.
- There exists an element of F which is not a sum of squares in F.
- If any sum of squares of elements of F equals zero, each element must equal zero.
- F can be totally ordered in such a way as to become an ordered field.
A formally real field with no formally real algebraic extension is a real closed field.
Last updated: 07-31-2005 17:59:09
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details