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Galois Theory, Coverings, and Riemann Surfaces / by Askold Khovanskii
Edition | 1st ed. 2013. |
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Publisher | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Year | 2013 |
Language | English |
Size | VIII, 81 p : online resource |
Authors | *Khovanskii, Askold author SpringerLink (Online service) |
Subjects | LCSH:Algebraic fields LCSH:Polynomials LCSH:Group theory LCSH:Topology LCSH:Algebra LCSH:Algebraic geometry FREE:Field Theory and Polynomials FREE:Group Theory and Generalizations FREE:Topology FREE:Algebra FREE:Algebraic Geometry |
Notes | 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 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 HTTP:URL=https://doi.org/10.1007/978-3-642-38841-5 |
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E-Book | Location | Media type | Volume | Call No. | Status | Reserve | Comments | ISBN | Printed | Restriction | Designated Book | Barcode No. |
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E-Book | オンライン | 電子ブック |
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Springer eBooks | 9783642388415 |
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電子リソース |
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EB00237996 |
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Material Type | E-Book |
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Classification | LCC:QA247-247.45 LCC:QA161.P59 DC23:512.3 |
ID | 4000117882 |
ISBN | 9783642388415 |
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