Published Online: May 11, 2017
Page range: 63 - 72
Received: Mar 17, 2017
DOI: https://doi.org/10.1515/forma-2017-0006
Keywords
© by Christoph Schwarzweller
This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License.
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].