Ordered rings and fields

Christoph Schwarzweller

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].
Author Christoph Schwarzweller II
Christoph Schwarzweller,,
- Institute of Informatics
Other language title versions
Journal seriesFormalized Mathematics, ISSN 1426-2630, e-ISSN 1898-9934
Issue year2017
Vol25
No1
Pages63-72
Publication size in sheets0.5
Keywords in Englishcommutative algebra, ordered fields, positive cones
DOIDOI:10.1515/forma-2017-0006
URL https://www.degruyter.com/downloadpdf/j/forma.2017.25.issue-1/forma-2017-0006/forma-2017-0006.xml
Languageen angielski
LicenseJournal (articles only); published final; Uznanie Autorstwa (CC-BY); with publication
Score (nominal)12
ScoreMinisterial score = 12.0, 15-12-2017, ArticleFromJournal
Ministerial score (2013-2016) = 12.0, 15-12-2017, ArticleFromJournal
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