rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Galois Theory, Coverings, and Riemann Surfaces
  name:
    name part: Khovanskii, Askold.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VIII, 81 p. online resource.
  abstract: 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.
  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.
  note: by Askold Khovanskii.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Algebraic geometry
  subject:
    topic: Field theory (Physics)
  subject:
    topic: Group theory
  subject:
    topic: Topology
  subject:
    topic: Mathematics
  subject:
    topic: Field Theory and Polynomials
  subject:
    topic: Group Theory and Generalizations
  subject:
    topic: Topology
  subject:
    topic: Algebra
  subject:
    topic: Algebraic Geometry
  classification: QA161.A-161.Z
  classification: QA161.P59
  classification: 512.3
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783642388415
  identifier: http://dx.doi.org/10.1007/978-3-642-38841-5
  record info:
    record creation date: 130911
    record change date: 20151204141151.0
    record identifier: 978-3-642-38841-5