Abstract
In this chapter we deal with the basic theory of ordered fields. In particular, we show that every ordered field admits a uniquely determined “real closure.” In the theory of ordered fields, this real closure plays essentially the same role as that played by the algebraic closure in the theory of fields. In the exercises at the end of this chapter we shall give several methods to construct ordered fields.
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© 2001 Springer-Verlag Berlin Heidelberg
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Prestel, A., Delzell, C.N. (2001). Real Fields. In: Positive Polynomials. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04648-7_2
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DOI: https://doi.org/10.1007/978-3-662-04648-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07445-5
Online ISBN: 978-3-662-04648-7
eBook Packages: Springer Book Archive