Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji:
http://hdl.handle.net/11320/13667
Pełny rekord metadanych
Pole DC | Wartość | Język |
---|---|---|
dc.contributor.author | Schwarzweller, Christoph | - |
dc.contributor.author | Rowińska-Schwarzweller, Agnieszka | - |
dc.date.accessioned | 2022-07-25T06:47:08Z | - |
dc.date.available | 2022-07-25T06:47:08Z | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | Formalized Mathematics, Volume 29, Issue 4, Pages 229-240 | pl |
dc.identifier.issn | 1426-2630 | - |
dc.identifier.uri | http://hdl.handle.net/11320/13667 | - |
dc.description.abstract | In this article we further develop field theory [6], [7], [12] in Mizar [1], [2], [3]: we deal with quadratic polynomials and quadratic extensions [5], [4]. First we introduce quadratic polynomials, their discriminants and prove the midnight formula. Then we show that - in case the discriminant of p being non square - adjoining a root of p’s discriminant results in a splitting field of p. Finally we prove that these are the only field extensions of degree 2, e.g. that an extension E of F is quadratic if and only if there is a non square Element a ∈ F such that E and F(√a) are isomorphic over F. | pl |
dc.language.iso | en | pl |
dc.publisher | DeGruyter Open | pl |
dc.rights | Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) | pl |
dc.rights.uri | https://creativecommons.org/licenses/by-sa/3.0/ | pl |
dc.subject | field extensions | pl |
dc.subject | quadratic polynomials | pl |
dc.subject | quadratic extensions | pl |
dc.title | Quadratic Extensions | pl |
dc.type | Article | pl |
dc.rights.holder | © 2021 University of Białymstoku | pl |
dc.rights.holder | CC-BY-SA License ver. 3.0 or later | pl |
dc.identifier.doi | 10.2478/forma-2021-0021 | - |
dc.description.Affiliation | Christoph Schwarzweller - Institute of Informatics, University of Gdańsk, Poland | pl |
dc.description.Affiliation | Agnieszka Rowińska-Schwarzweller - Sopot, Poland | pl |
dc.description.references | Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, 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. | pl |
dc.description.references | Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6. | pl |
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 Information Systems (FedCSIS), volume 8 of Annals of Computer Science and Information Systems, pages 363–371, 2016. doi:10.15439/2016F520. | pl |
dc.description.references | Nathan Jacobson. Basic Algebra I. Dover Books on Mathematics, 1985. | pl |
dc.description.references | Serge Lang. Algebra. Springer Verlag, 2002 (Revised Third Edition). | pl |
dc.description.references | Heinz Luneburg. Gruppen, Ringe, K¨orper: Die grundlegenden Strukturen der Algebra. Oldenbourg Verlag, 1999. | pl |
dc.description.references | Knut Radbruch. Algebra I. Lecture Notes, University of Kaiserslautern, Germany, 1991. | pl |
dc.description.references | Christoph Schwarzweller. Ring and field adjunctions, algebraic elements and minimal polynomials. Formalized Mathematics, 28(3):251–261, 2020. doi:10.2478/forma-2020-0022. | pl |
dc.description.references | Christoph Schwarzweller. Formally real fields. Formalized Mathematics, 25(4):249–259, 2017. doi:10.1515/forma-2017-0024. | pl |
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. | pl |
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. | pl |
dc.description.references | Steven H. Weintraub. Galois Theory. Springer-Verlag, 2 edition, 2009. | pl |
dc.identifier.eissn | 1898-9934 | - |
dc.description.volume | 29 | pl |
dc.description.issue | 4 | pl |
dc.description.firstpage | 229 | pl |
dc.description.lastpage | 240 | pl |
dc.identifier.citation2 | Formalized Mathematics | pl |
dc.identifier.orcid | 0000-0001-9587-8737 | - |
Występuje w kolekcji(ach): | Formalized Mathematics, 2021, Volume 29, Issue 4 |
Pliki w tej pozycji:
Plik | Opis | Rozmiar | Format | |
---|---|---|---|---|
10.2478_forma-2021-0021.pdf | 285,35 kB | Adobe PDF | Otwórz |
Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL