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03397nam a22004935i 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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OSt |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20140310151459.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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130911s2013 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783642388415 |
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978-3-642-38841-5 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA161.A-161.Z |
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| Classification number |
QA161.P59 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
512.3 |
| Edition number |
23 |
| 264 #1 - |
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| -- |
Berlin, Heidelberg : |
| -- |
Springer Berlin Heidelberg : |
| -- |
Imprint: Springer, |
| -- |
2013. |
| 912 ## - |
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| -- |
ZDB-2-SMA |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Khovanskii, Askold. |
| Relator term |
author. |
| 245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
|---|
| Title |
Galois Theory, Coverings, and Riemann Surfaces |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc |
by Askold Khovanskii. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
VIII, 81 p. |
| Other physical details |
online resource. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
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 ## - SUMMARY, ETC. |
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| Summary, etc |
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 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Mathematics. |
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| Topical term or geographic name as entry element |
Algebra. |
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| Topical term or geographic name as entry element |
Geometry, algebraic. |
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| Topical term or geographic name as entry element |
Field theory (Physics). |
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| Topical term or geographic name as entry element |
Group theory. |
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| Topical term or geographic name as entry element |
Topology. |
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| Topical term or geographic name as entry element |
Mathematics. |
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| Topical term or geographic name as entry element |
Field Theory and Polynomials. |
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| Topical term or geographic name as entry element |
Group Theory and Generalizations. |
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| Topical term or geographic name as entry element |
Topology. |
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| Topical term or geographic name as entry element |
Algebra. |
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| Topical term or geographic name as entry element |
Algebraic Geometry. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Printed edition: |
| International Standard Book Number |
9783642388408 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-3-642-38841-5 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
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| Item type |
E-Book |
