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http://hdl.handle.net/11320/19734Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Schwarzweller, Christoph | - |
| dc.contributor.author | Rowińska-Schwarzweller, Agnieszka | - |
| dc.date.accessioned | 2026-02-02T09:32:48Z | - |
| dc.date.available | 2026-02-02T09:32:48Z | - |
| dc.date.issued | 2025 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 33, Issue 1, Pages 175-183 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/19734 | - |
| dc.description.abstract | This article continues a series devoted to the formalization of the Fundamental Theorem of Galois Theory using the Mizar proof assistant. We define groups of automorphisms and fixed fields and establish their fundamental properties. We also introduce an encoding of conjugates for groups of automorphisms and Galois extensions, and present the classical example demonstrating that the field of complex numbers is a Galois extension of the field of real numbers. | pl |
| dc.language.iso | en | pl |
| dc.publisher | University of Białystok | pl |
| dc.rights | Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) | pl |
| dc.rights.uri | https://creativecommons.org/licenses/by-sa/4.0/ | pl |
| dc.subject | Galois theory | pl |
| dc.subject | conjugates | pl |
| dc.subject | field of complex numbers | pl |
| dc.subject | finite field | pl |
| dc.title | Introduction to Galois Theory | pl |
| dc.type | Article | pl |
| dc.rights.holder | 2025 The Author(s) | pl |
| dc.rights.holder | CC BY-SA 4.0 license | pl |
| dc.identifier.doi | 10.2478/forma-2025-0014 | - |
| dc.description.Affiliation | Christoph Schwarzweller -Institute of Informatics, University of Gdańsk, Poland | pl |
| dc.description.Affiliation | Agnieszka Rowińska-Schwarzweller - Institute of Informatics, University of Gdańsk, Poland | pl |
| dc.description.references | David S. Dummit and Richard M. Foote. Abstract Algebra. Wiley and Sons, third edition, 2004. | pl |
| dc.description.references | Andreas Gathmann. Einfuhrung in die Algebra. Lecture Notes, University of Kaiserslautern, Germany, 2011. | pl |
| 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. | 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 | I. Martin Isaacs. Algebra: A Graduate Course. Wadsworth Inc., 1994. | pl |
| dc.description.references | Serge Lang. Algebra (Revised Third Edition). Springer Verlag, 2002. | pl |
| dc.description.references | Knut Radbruch. Algebra I. Lecture Notes, University of Kaiserslautern, Germany, 1991. | pl |
| dc.description.references | Colin Rothgang, Artur Korniłowicz, and Florian Rabe. A new export of the Mizar Mathematical Library. In Fairouz Kamareddine and Claudio Sacerdoti Coen, editors, Intelligent Computer Mathematics, pages 205–210, Cham, 2021. Springer International Publishing. doi:10.1007/978-3-030-81097-9_17. | pl |
| dc.description.references | Christoph Schwarzweller. Finite fields. Formalized Mathematics, 32(1):289–302, 2024. doi:10.2478/forma-2024-0024. | pl |
| dc.description.references | Christoph Schwarzweller and Agnieszka Rowińska-Schwarzweller. The lattice of intermediate fields and other preliminaries to Galois theory. Formalized Mathematics, 33(1): 165–174, 2025. doi:10.2478/forma-2025-0013. | pl |
| dc.description.references | Ian Stewart. Galois Theory. Chapman and Hall/CRC, fourth edition, 2015. | pl |
| dc.description.references | Steven H. Weintraub. Galois Theory. Springer-Verlag, second edition, 2009. | pl |
| dc.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 33 | pl |
| dc.description.issue | 1 | pl |
| dc.description.firstpage | 175 | pl |
| dc.description.lastpage | 183 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| dc.identifier.orcid | 0000-0001-9587-8737 | - |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2025, Volume 33, Issue 1 | |
Pliki w tej pozycji:
| Plik | Opis | Rozmiar | Format | |
|---|---|---|---|---|
| Introduction_to_Galois_Theory.pdf | 244,05 kB | Adobe PDF | Otwórz |
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