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|a 9783642388415
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|a Khovanskii, Askold
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|a Galois Theory, Coverings, and Riemann Surfaces
|h Elektronische Ressource
|c by Askold Khovanskii
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| 250 |
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|a 1st ed. 2013
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 2013, 2013
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| 300 |
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|a VIII, 81 p
|b online resource
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|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
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| 653 |
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|a Group Theory and Generalizations
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| 653 |
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|a Algebraic Geometry
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| 653 |
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|a Group theory
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| 653 |
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|a Algebraic fields
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| 653 |
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|a Field Theory and Polynomials
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| 653 |
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|a Topology
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| 653 |
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|a Algebra
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| 653 |
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|a Algebraic geometry
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| 653 |
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|a Polynomials
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| 041 |
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|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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|a 10.1007/978-3-642-38841-5
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| 856 |
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|u https://doi.org/10.1007/978-3-642-38841-5?nosfx=y
|x Verlag
|3 Volltext
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|a 512.3
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| 520 |
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|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
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