Ordered Rings and Fields

Christoph Schwarzweller

doi:10.1515/forma-2017-0006

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Ordered Rings and Fields

Formalized Mathematics

Volume 25 (2017): Issue 1 (March 2017)

By: Christoph Schwarzweller

Open Access

|May 2017

Abstract

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].

References

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Articles in this issue

DOI: https://doi.org/10.1515/forma-2017-0006 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

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Language: English

Page range: 63 - 72

Submitted on: Mar 17, 2017

Published on: May 11, 2017

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

12J15,

03B35

Related subjects:

Computer sciences,

Computer sciences, other,

Mathematics,

General mathematics

© 2017 Christoph Schwarzweller, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.

Volume 25 (2017): Issue 1 (March 2017)