Ordered rings and fields

Christoph Schwarzweller


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 (FMPI / II)
Christoph Schwarzweller,,
- Institute of Informatics
Journal seriesFormalized Mathematics, ISSN 1426-2630, e-ISSN 1898-9934, (B 12 pkt)
Issue year2017
Publication size in sheets0.5
Keywords in Englishcommutative algebra, ordered fields, positive cones
ASJC Classification2604 Applied Mathematics; 2605 Computational Mathematics
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 - Na Tych Samych Warunkach (CC-BY-SA); with publication
Score (nominal)12
Score sourcejournalList
ScoreMinisterial score = 12.0, 06-02-2020, ArticleFromJournal
Publication indicators WoS Citations = 1; Scopus SNIP (Source Normalised Impact per Paper): 2017 = 0.236
Citation count*1 (2020-05-30)
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