Ordered rings and fields
AbstractWe 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].
|Other language title versions|
|Journal series||Formalized Mathematics, ISSN 1426-2630, e-ISSN 1898-9934|
|Publication size in sheets||0.5|
|Keywords in English||commutative algebra, ordered fields, positive cones|
|License||Journal (articles only); published final; ; with publication|
|Score|| = 12.0, 15-12-2017, ArticleFromJournal|
= 12.0, 15-12-2017, ArticleFromJournal
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