Order and valuations

R. Kochendörffer
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R. Kochendörffer: University of Dortmund

Chapter 8 in Introduction to Algebra, 1972, pp 267-284 from Springer

Abstract: Abstract In the field of the real numbers —1 cannot be expressed as a sum of squares. This property of the real numbers has been used by E. Artin and O. Schreier to develop a theory of so-called formally real fields. It turns out that precisely in the formally real fields one can introduce a complete order with the familiar properties with respect to addition and multiplication. Moreover, we shall generalize the concept of the absolute value to obtain the so-called valuations. In several branches of algebra the theory of valuations is an indispensabel tool. We must confine ourselves to the very rudiments of this theory.

Date: 1972
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DOI: 10.1007/978-94-009-8179-9_8

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