<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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].</p></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].

Ordered Rings and Fields

Formalized Mathematics

This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License.

{"article-title":"Ordered Rings and Fields"}

We introduce ordered rings and fields following Artin-Schreier’s approach using positive cones. We show that such orderings coincide with total order relations...

Ordered Rings and Fields

Online veröffentlicht: 11. Mai 2017

Seitenbereich: 63 - 72

Eingereicht: 17. März 2017

DOI: https://doi.org/10.1515/forma-2017-0006

Schlüsselwörter
commutative algebra, ordered fields, positive cones

© by Christoph Schwarzweller

This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License.

Ordered Rings and Fields

Online veröffentlicht: 11. Mai 2017

Seitenbereich: 63 - 72

Eingereicht: 17. März 2017

DOI: https://doi.org/10.1515/forma-2017-0006

Schlüsselwörtercommutative algebra, ordered fields, positive cones

© by Christoph Schwarzweller

This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License.

Schlüsselwörter
commutative algebra, ordered fields, positive cones