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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2013.
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| Edición: | 1st ed. 2013. |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
|---|---|---|---|
| 001 | 978-3-642-38841-5 | ||
| 003 | DE-He213 | ||
| 005 | 20220113004935.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 130911s2013 gw | s |||| 0|eng d | ||
| 020 | |a 9783642388415 |9 978-3-642-38841-5 | ||
| 024 | 7 | |a 10.1007/978-3-642-38841-5 |2 doi | |
| 050 | 4 | |a QA247-247.45 | |
| 050 | 4 | |a QA161.P59 | |
| 072 | 7 | |a PBF |2 bicssc | |
| 072 | 7 | |a MAT002010 |2 bisacsh | |
| 072 | 7 | |a PBF |2 thema | |
| 082 | 0 | 4 | |a 512.3 |2 23 |
| 100 | 1 | |a Khovanskii, Askold. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Galois Theory, Coverings, and Riemann Surfaces |h [electronic resource] / |c by Askold Khovanskii. |
| 250 | |a 1st ed. 2013. | ||
| 264 | 1 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg : |b Imprint: Springer, |c 2013. | |
| 300 | |a VIII, 81 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 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. | |
| 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 | 0 | |a Algebraic fields. | |
| 650 | 0 | |a Polynomials. | |
| 650 | 0 | |a Group theory. | |
| 650 | 0 | |a Topology. | |
| 650 | 0 | |a Algebra. | |
| 650 | 0 | |a Algebraic geometry. | |
| 650 | 1 | 4 | |a Field Theory and Polynomials. |
| 650 | 2 | 4 | |a Group Theory and Generalizations. |
| 650 | 2 | 4 | |a Topology. |
| 650 | 2 | 4 | |a Algebra. |
| 650 | 2 | 4 | |a Algebraic Geometry. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783642388422 |
| 776 | 0 | 8 | |i Printed edition: |z 9783642388408 |
| 776 | 0 | 8 | |i Printed edition: |z 9783662519561 |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-642-38841-5 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||