Formally Real Fields

Pole DC	Wartość	Język
dc.contributor.author	Schwarzweller, Christoph	-
dc.date.accessioned	2018-05-11T07:20:20Z	-
dc.date.available	2018-05-11T07:20:20Z	-
dc.date.issued	2017	-
dc.identifier.citation	Formalized Mathematics, Volume 25, Issue 4, Pages 249–259	-
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/6550	-
dc.description.abstract	Summary We extend the algebraic theory of ordered fields [7, 6] in Mizar [1, 2, 3]: we show that every preordering can be extended into an ordering, i.e. that formally real and ordered fields coincide.We further prove some characterizations of formally real fields, in particular the one by Artin and Schreier using sums of squares [4]. In the second part of the article we define absolute values and the square root function [5].	-
dc.language.iso	en	-
dc.publisher	DeGruyter Open	-
dc.subject	formally real fields	-
dc.subject	ordered fields	-
dc.subject	abstract value	-
dc.subject	square roots	-
dc.title	Formally Real Fields	-
dc.type	Article	-
dc.identifier.doi	10.1515/forma-2017-0024	-
dc.description.Affiliation	Institute of Informatics, Faculty of Mathematics, Physics and Informatics, University of Gdansk Wita Stwosza 57, 80-308 Gdansk, Poland	-
dc.description.references	Grzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261-279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi: 10.1007/978-3-319-20615-8 17.	-
dc.description.references	Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191-198, 2015. doi: 10.1007/s10817-015-9345-1.	-
dc.description.references	Adam Grabowski, Artur Korniłowicz, and Christoph Schwarzweller. On algebraic hierarchies in mathematical repository of Mizar. In M. Ganzha, L. Maciaszek, and M. Paprzycki, editors, Proceedings of the 2016 Federated Conference on Computer Science and Infor mation Systems (FedCSIS), volume 8 of Annals of Computer Science and Information Systems, pages 363-371, 2016. doi: 10.15439/2016F520.	-
dc.description.references	Nathan Jacobson. Lecture Notes in Abstract Algebra, III. Theory of Fields and Galois Theory. Springer-Verlag, 1964.	-
dc.description.references	Manfred Knebusch and Claus Scheiderer. Einf¨uhrung in die reelle Algebra. Vieweg-Verlag, 1989.	-
dc.description.references	Alexander Prestel. Lectures on Formally Real Fields. Springer-Verlag, 1984.	-
dc.description.references	Knut Radbruch. Geordnete K¨orper. Lecture Notes, University of Kaiserslautern, Germany, 1991.	-
dc.description.references	Christoph Schwarzweller. The binomial theorem for algebraic structures. Formalized Mathematics, 9(3):559-564, 2001.	-
dc.description.references	Christoph Schwarzweller. Ordered rings and fields. Formalized Mathematics, 25(1):63-72, 2017. doi: 10.1515/forma-2017-0006.	-
dc.description.references	Christoph Schwarzweller. On roots of polynomials and algebraically closed fields. Formalized Mathematics, 25(3):185-195, 2017. doi: 10.1515/forma-2017-0018.	-
dc.description.references	Christoph Schwarzweller and Artur Korniłowicz. Characteristic of rings. Prime fields. Formalized Mathematics, 23(4):333-349, 2015. doi: 10.1515/forma-2015-0027.	-
dc.identifier.eissn	1898-9934	-
dc.description.volume	25	-
dc.description.issue	4	-
dc.description.firstpage	249	-
dc.description.lastpage	259	-
dc.identifier.citation2	Formalized Mathematics	-
Występuje w kolekcji(ach):	Formalized Mathematics, 2017, Volume 25, Issue 4

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