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The Resource Galois Theory, Coverings, and Riemann Surfaces, by Askold Khovanskii, (electronic resource)
Galois Theory, Coverings, and Riemann Surfaces, by Askold Khovanskii, (electronic resource)
Resource Information
The item Galois Theory, Coverings, and Riemann Surfaces, by Askold Khovanskii, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Galois Theory, Coverings, and Riemann Surfaces, by Askold Khovanskii, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 The first part of this book provides an elementary and selfcontained 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 selfcontained 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
 Language

 eng
 eng
 Edition
 1st ed. 2013.
 Extent
 1 online resource (86 p.)
 Note
 Description based upon print version of record
 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 kSolvable Group and Representability by kRadicals
 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 kRadicals
 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
 Isbn
 9783642388415
 Label
 Galois Theory, Coverings, and Riemann Surfaces
 Title
 Galois Theory, Coverings, and Riemann Surfaces
 Statement of responsibility
 by Askold Khovanskii
 Language

 eng
 eng
 Summary
 The first part of this book provides an elementary and selfcontained 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 selfcontained 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://library.link/vocab/creatorName
 Khovanskii, Askold
 Dewey number

 510
 512
 512.2
 512.3
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 RFIyCUnJRs
 Language note
 English
 LC call number
 QA247QA247.45
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/subjectName

 Field theory (Physics)
 Group theory
 Topology
 Algebra
 Geometry, algebraic
 Field Theory and Polynomials
 Group Theory and Generalizations
 Topology
 Algebra
 Algebraic Geometry
 Label
 Galois Theory, Coverings, and Riemann Surfaces, by Askold Khovanskii, (electronic resource)
 Note
 Description based upon print version of record
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 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 kSolvable Group and Representability by kRadicals  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 kRadicals  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
 Dimensions
 unknown
 Edition
 1st ed. 2013.
 Extent
 1 online resource (86 p.)
 Form of item
 online
 Isbn
 9783642388415
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/9783642388415
 Specific material designation
 remote
 System control number

 (CKB)3710000000019125
 (EBL)1466266
 (SSID)ssj0001010499
 (PQKBManifestationID)11562136
 (PQKBTitleCode)TC0001010499
 (PQKBWorkID)10999791
 (PQKB)11138951
 (DEHe213)9783642388415
 (EXLCZ)993710000000019125
 Label
 Galois Theory, Coverings, and Riemann Surfaces, by Askold Khovanskii, (electronic resource)
 Note
 Description based upon print version of record
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 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 kSolvable Group and Representability by kRadicals  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 kRadicals  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
 Dimensions
 unknown
 Edition
 1st ed. 2013.
 Extent
 1 online resource (86 p.)
 Form of item
 online
 Isbn
 9783642388415
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/9783642388415
 Specific material designation
 remote
 System control number

 (CKB)3710000000019125
 (EBL)1466266
 (SSID)ssj0001010499
 (PQKBManifestationID)11562136
 (PQKBTitleCode)TC0001010499
 (PQKBWorkID)10999791
 (PQKB)11138951
 (DEHe213)9783642388415
 (EXLCZ)993710000000019125
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/GaloisTheoryCoveringsandRiemannSurfaces/hxMh_oKCMPk/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/GaloisTheoryCoveringsandRiemannSurfaces/hxMh_oKCMPk/">Galois Theory, Coverings, and Riemann Surfaces, by Askold Khovanskii, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>