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http://hdl.handle.net/11320/19733Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Schwarzweller, Christoph | - |
| dc.contributor.author | Rowińska-Schwarzweller, Agnieszka | - |
| dc.date.accessioned | 2026-02-02T09:10:42Z | - |
| dc.date.available | 2026-02-02T09:10:42Z | - |
| dc.date.issued | 2025 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 33, Issue 1, Pages 165-174 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/19733 | - |
| dc.description.abstract | This article initiates a series devoted to the formalization of the Fundamental Theorem of Galois Theory. It presents several preliminaries required for the formal development of Galois theory. In particular, as a main result, we define the lattice of intermediate fields of an extension E/F; we also treat sets of functions, groups, and intermediate fields in order to provide the necessary cluster registrations that enable effective Mizar automation. | 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 | lattice of intermediate fields | pl |
| dc.subject | Galois connection | pl |
| dc.title | The Lattice of Intermediate Fields and Other Preliminaries 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-2025-0013 | - |
| 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 | Grzegorz Bancerek and Piotr Rudnicki. A Compendium of Continuous Lattices in Mizar. Journal of Automated Reasoning, 29(3–4):189–224, 2002. doi:10.1023/A:1021966832558. | pl |
| dc.description.references | Garrett Birkhoff. Lattice Theory. Providence, Rhode Island, New York, 1967. | pl |
| dc.description.references | David S. Dummit and Richard M. Foote. Abstract Algebra. Wiley and Sons, third edition, 2004. | pl |
| dc.description.references | Adam Grabowski. Mechanizing complemented lattices within Mizar system. Journal of Automated Reasoning, 55:211–221, 2015. doi:10.1007/s10817-015-9333-5. | 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 | George Gratzer. Lattice Theory: Foundation. Birkhauser, 2011. | 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 | Christoph Schwarzweller and Agnieszka Rowińska-Schwarzweller. Simple extensions. Formalized Mathematics, 31(1):287–298, 2023. doi:10.2478/forma-2023-0023. | 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 | 165 | pl |
| dc.description.lastpage | 174 | 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 | |
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|---|---|---|---|---|
| The_Lattice_of_Intermediate_Fields_and_Other_Preliminaries_to_Galois_Theory.pdf | 252,28 kB | Adobe PDF | Otwórz |
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