Galois theory, coverings, and Riemann surfaces
The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and th...
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | Livre numérique |
| اللغة: | Anglais |
| منشور في: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
2013.
Cham : Springer Nature |
| الموضوعات: | |
| الوصول للمادة أونلاين: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| ملاحظة: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Galois theory, coverings, and Riemann surfaces, Askold Khovanskii, Berlin, Springer, 2013, 1 vol. (VIII-81 p.), 978-3-642-38840-8 • Galois Theory, Coverings, and Riemann Surfaces, Texte imprimé, 9783642388422 • Galois Theory, Coverings, and Riemann Surfaces, Texte imprimé, 9783662519561 |
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|---|---|---|---|
| 001 | 947024 | ||
| 008 | 131018s2013 xx ||| |||| 00| 0 eng d | ||
| 009 | PPN172427428 | ||
| 020 | |a 9783642388415 | ||
| 041 | 1 | |a eng |h rus | |
| 082 | |a 512.3 | ||
| 084 | |a 55-02. 2010 | ||
| 084 | |a 12F10. 2010 | ||
| 084 | |a 30F10. 2010 | ||
| 100 | 1 | |a Hovanskij, Askol½d Georgievič. | |
| 245 | 1 | 0 | |a Galois theory, coverings, and Riemann surfaces |c Askold Khovanskii. |
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg. | ||
| 260 | |a Cham : |b Springer Nature, |c 2013. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 0 | |a Chapter 1 Galois Theory: 1.1 Action of a Solvable Group and Representability by Radicals -- 1.2 Fixed Points under an Action of a Finite Group and Its Subgroups -- 1.3 Field Automorphisms and Relations between Elements in a Field -- 1.4 Action of a k-Solvable Group and Representability by k-Radicals -- 1.5 Galois Equations -- 1.6 Automorphisms Connected with a Galois Equation -- 1.7 The Fundamental Theorem of Galois Theory -- 1.8 A Criterion for Solvability of Equations by Radicals -- 1.9 A Criterion for Solvability of Equations by k-Radicals -- 1.10 Unsolvability of Complicated Equations by Solving Simpler Equations -- 1.11 Finite Fields -- Chapter 2 Coverings: 2.1 Coverings over Topological Spaces -- 2.2 Completion of Finite Coverings over Punctured Riemann Surfaces -- Chapter 3 Ramified Coverings and Galois Theory: 3.1 Finite Ramified Coverings and Algebraic Extensions of Fields of Meromorphic Functions -- 3.2 Geometry of Galois Theory for Extensions of a Field of Meromorphic Functions -- References -- Index. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. chttps://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and the classification of coverings over a topological space. The third part contains a geometric description of finite algebraic extensions of the field of meromorphic functions on a Riemann surface and provides an introduction to the topological Galois theory developed by the author. All results are presented in the same elementary and self-contained manner as classical Galois theory, making this book both useful and interesting to readers with a variety of backgrounds in mathematics, from advanced undergraduate students to researchers. | ||
| 650 | |a Topologie algébrique | ||
| 650 | |a Galois, Théorie de | ||
| 650 | |a Surfaces de Riemann | ||
| 765 | 0 | |t Teoriya Galua, Nakrytiya i Rimanovy Poverkhnosti |d 2006 | |
| 776 | 0 | |0 175840830 |t Galois theory, coverings, and Riemann surfaces |f Askold Khovanskii |c Berlin |n Springer |d 2013 |p 1 vol. (VIII-81 p.) |z 978-3-642-38840-8 | |
| 776 | 0 | |t Galois Theory, Coverings, and Riemann Surfaces |b Texte imprimé |z 9783642388422 | |
| 776 | 0 | |t Galois Theory, Coverings, and Riemann Surfaces |b Texte imprimé |z 9783662519561 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/978-3-642-38841-5 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-15MXJPDR-V |z Accès sur la plateforme Istex | |
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| 856 | 4 | |5 180339901:750833904 |u https://ezproxy.insa-cvl.fr/login?qurl=https://doi.org/10.1007/978-3-642-38841-5 |z Accès INSA CVL | |
| 997 | |0 947024 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||