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http://hdl.handle.net/11320/6550
Pełny rekord metadanych
Pole DC | Wartość | Język |
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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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forma-2017-0024.pdf | 301,73 kB | Adobe PDF | Otwórz |
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