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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 Boston University 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 Boston University 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
 Extent
 VIII, 81 p.
 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
 Subject

 Algebra
 Topology
 Field Theory and Polynomials
 Algebra
 Group Theory and Generalizations
 Field theory (Physics)
 Geometry, algebraic
 Field theory (Physics)
 Geometry, algebraic
 Geometry, algebraic
 Algebraic Geometry
 Mathematics
 Mathematics
 Field theory (Physics)
 Algebra
 Topology
 Group theory
 Topology
 Electronic resources
 Mathematics
 Group theory
 Group theory
 Language
 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
 Image bit depth
 0
 LC call number

 QA161.A161.Z
 QA161.P59
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink
 http://library.link/vocab/subjectName

 Mathematics
 Algebra
 Geometry, algebraic
 Field theory (Physics)
 Group theory
 Topology
 Mathematics
 Field Theory and Polynomials
 Group Theory and Generalizations
 Topology
 Algebra
 Algebraic Geometry
 Label
 Galois Theory, Coverings, and Riemann Surfaces, by Askold Khovanskii, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 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
 Extent
 VIII, 81 p.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783642388415
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783642388415
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783642388415
 Label
 Galois Theory, Coverings, and Riemann Surfaces, by Askold Khovanskii, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 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
 Extent
 VIII, 81 p.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783642388415
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783642388415
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783642388415
Subject
 Algebra
 Algebra
 Algebra
 Algebraic Geometry
 Electronic resources
 Field Theory and Polynomials
 Field theory (Physics)
 Field theory (Physics)
 Field theory (Physics)
 Geometry, algebraic
 Geometry, algebraic
 Geometry, algebraic
 Group Theory and Generalizations
 Group theory
 Group theory
 Group theory
 Mathematics
 Mathematics
 Mathematics
 Topology
 Topology
 Topology
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.bu.edu/portal/GaloisTheoryCoveringsandRiemannSurfaces/jN2G74EE3WY/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bu.edu/portal/GaloisTheoryCoveringsandRiemannSurfaces/jN2G74EE3WY/">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.bu.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.bu.edu/">Boston University Libraries</a></span></span></span></span></div>