Formally real field

From Wikipedia, the free encyclopedia

You have new messages (last change).

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.
  • If any sum of squares of elements of F equals zero, each of those elements 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.

Retrieved from "http://en.wikipedia.org../../../f/o/r/Formally_real_field.html"
In other languages