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Author:   Askold Khovanskii ,  Vladlen Timorin ,  Valentina Kiritchenko
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 2013
Dimensions:   Width: 15.50cm , Height: 0.50cm , Length: 23.50cm
Weight:   1.591kg
ISBN:  

9783662519561

ISBN 10:   3662519569
Pages:   81
Publication Date:   23 August 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.
Language:   English

Table of Contents

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

Reviews

From the reviews: “This book features generalizations and variations beyond Abel’s theorem per se. … This book is for those who appreciate concision, and remarkably, the author develops these extended results in full detail--all in a work just a fraction of the length of standard Galois theory textbooks. Summing Up: Recommended. Upper-division undergraduates through researchers/faculty.” (D. V. Feldman, Choice, Vol. 51 (10), June, 2014)

From the reviews: This book features generalizations and variations beyond Abel's theorem per se. ... This book is for those who appreciate concision, and remarkably, the author develops these extended results in full detail--all in a work just a fraction of the length of standard Galois theory textbooks. Summing Up: Recommended. Upper-division undergraduates through researchers/faculty. (D. V. Feldman, Choice, Vol. 51 (10), June, 2014)

Author Information

Askold Khovanskii is a Professor of Mathematics at the University of Toronto, and a principal researcher at the RAS Institute for Systems Analysis (Moscow, Russia). He is a founder of Topological Galois Theory and the author of fundamental results in this area.

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