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Displaying similar documents to “Pathological functions on Puiseux series ordered fields and others.”

Ordered Rings and Fields

Christoph Schwarzweller (2017)

Formalized Mathematics

Similarity:

We introduce ordered rings and fields following Artin-Schreier’s approach using positive cones. We show that such orderings coincide with total order relations and give examples of ordered (and non ordered) rings and fields. In particular we show that polynomial rings can be ordered in (at least) two different ways [8, 5, 4, 9]. This is the continuation of the development of algebraic hierarchy in Mizar [2, 3].