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http://hdl.handle.net/11320/17809Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Schwarzweller, Christoph | - |
| dc.date.accessioned | 2025-01-10T12:08:08Z | - |
| dc.date.available | 2025-01-10T12:08:08Z | - |
| dc.date.issued | 2024 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 32, Issue 1, Pages 289–302 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/17809 | - |
| dc.description.abstract | We continue the formalization of field theory in Mizar. Here we prove existence and uniqueness of finite fields by constructing the splitting field of the polynomial X (pⁿ) −X over the prime field of a field with characteristic p. We also define the Frobenius morphism and show that the automorphisms of a field with pⁿ elements are exactly the powers 0, . . . , n − 1 of the Frobenius morphism, that is the automorphism group is generated by the Frobenius morphism. | 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 | finite field | pl |
| dc.subject | splitting field | pl |
| dc.subject | Galois field | pl |
| dc.title | Finite Fields | pl |
| dc.type | Article | pl |
| dc.rights.holder | © 2024 The Author(s) | pl |
| dc.rights.holder | CC BY-SA 3.0 license | pl |
| dc.identifier.doi | 10.2478/forma-2024-0024 | - |
| dc.description.Affiliation | Institute of Informatics, University of Gdańsk, 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. Equality in computer proof-assistants. In Ganzha, Maria and Maciaszek, Leszek and Paprzycki, Marcin, editor, Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, volume 5 of ACSIS-Annals of Computer Science and Information Systems, pages 45–54. IEEE, 2015. doi:10.15439/2015F229. | 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 | Emin Karayel. Finite fields. Archive of Formal Proofs, 2022. https://isa-afp.org/entries/Finite_Fields.html, Formal proof development. | pl |
| dc.description.references | Artur Korniłowicz. Flexary connectives in Mizar. Computer Languages, Systems & Structures, 44:238–250, December 2015. doi:10.1016/j.cl.2015.07.002. | pl |
| dc.description.references | Artur Korniłowicz and Christoph Schwarzweller. The first isomorphism theorem and other properties of rings. Formalized Mathematics, 22(4):291–301, 2014. doi:10.2478/forma-2014-0029. | 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. Existence and uniqueness of algebraic closures. Formalized Mathematics, 30(4):281–294, 2022. doi:10.2478/forma-2022-0022. | pl |
| dc.description.references | Christoph Schwarzweller. Normal extensions. Formalized Mathematics, 31(1):121–130, 2023. doi:10.2478/forma-2023-0011. | 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.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 32 | pl |
| dc.description.issue | 1 | pl |
| dc.description.firstpage | 289 | pl |
| dc.description.lastpage | 302 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| dc.identifier.orcid | 0000-0001-9587-8737 | - |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2024, Volume 32, Issue 1 | |
Pliki w tej pozycji:
| Plik | Opis | Rozmiar | Format | |
|---|---|---|---|---|
| Finite-Fields.pdf | 310,3 kB | Adobe PDF | Otwórz |
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