Characterization of Finite Galois Extensions

Pole DC	Wartość	Język
dc.contributor.author	Schwarzweller, Christoph	-
dc.date.accessioned	2026-02-02T13:13:16Z	-
dc.date.available	2026-02-02T13:13:16Z	-
dc.date.issued	2025	-
dc.identifier.citation	Formalized Mathematics, Volume 33, Issue 1, Pages 237-244	pl
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/19739	-
dc.description.abstract	In this article we prove the well-known characterization of finite Galois extensions: a finite extension E of F is a Galois extension of F iff E is both normal and separable iff E is the splitting field of a separable polynomial p ∈ F[X]. We also prove some applications of the characterization, so for example that F(a1, . . . , an) is a separable extension of F if and only if all the ai are separable, or that every finite separable extension of F is contained in a Galois extension of F.	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	finite Galois extension	pl
dc.subject	minimal polynomial	pl
dc.subject	separable extension	pl
dc.title	Characterization of Finite Galois Extensions	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-2025-0019	-
dc.description.Affiliation	Institute of Informatics, University of Gdańsk, Poland	pl
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dc.description.references	Christoph Schwarzweller and Agnieszka Rowińska-Schwarzweller. Introduction to Galois theory. Formalized Mathematics, 33(1):175–183, 2025. doi:10.2478/forma-2025-0014.	pl
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dc.identifier.eissn	1898-9934	-
dc.description.volume	33	pl
dc.description.issue	1	pl
dc.description.firstpage	237	pl
dc.description.lastpage	244	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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