Skip to main content
SpringerLink
Log in
Birkhäuser

Introduction to the Galois Correspondence

  • Textbook
  • © 1998

Overview

Authors:
  1. Maureen H. Fenrick

    1. Department of Mathematics, Astronomy and Statistics, Mankato State University, Mankato, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (4 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Preliminaries — Groups and Rings

    • Maureen H. Fenrick
    Pages 1-72

  3. Field Extensions

    • Maureen H. Fenrick
    Pages 73-109

  4. The Galois Correspondence

    • Maureen H. Fenrick
    Pages 110-162

  5. Applications

    • Maureen H. Fenrick
    Pages 163-187

  6. Back Matter

    Pages 188-244
    Download chapter PDF
Back to top

Keywords

About this book

In this presentation of the Galois correspondence, modern theories of groups and fields are used to study problems, some of which date back to the ancient Greeks. The techniques used to solve these problems, rather than the solutions themselves, are of primary importance. The ancient Greeks were concerned with constructibility problems. For example, they tried to determine if it was possible, using straightedge and compass alone, to perform any of the following tasks? (1) Double an arbitrary cube; in particular, construct a cube with volume twice that of the unit cube. (2) Trisect an arbitrary angle. (3) Square an arbitrary circle; in particular, construct a square with area 1r. (4) Construct a regular polygon with n sides for n > 2. If we define a real number c to be constructible if, and only if, the point (c, 0) can be constructed starting with the points (0,0) and (1,0), then we may show that the set of constructible numbers is a subfield of the field R of real numbers containing the field Q of rational numbers. Such a subfield is called an intermediate field of Rover Q. We may thus gain insight into the constructibility problems by studying intermediate fields of Rover Q. In chapter 4 we will show that (1) through (3) are not possible and we will determine necessary and sufficient conditions that the integer n must satisfy in order that a regular polygon with n sides be constructible.

Reviews

"It is the clearest this reviewer has ever seen... Particularly remarkable is the author's avoidance of all temptations to give pretty proofs of neatly arranged theorems at the cost of clarity... Highly recommended".

--Gian-Carlo Rota

Authors and Affiliations

  • Department of Mathematics, Astronomy and Statistics, Mankato State University, Mankato, USA

    Maureen H. Fenrick

Bibliographic Information

  • Book Title: Introduction to the Galois Correspondence

  • Authors: Maureen H. Fenrick

  • DOI: https://doi.org/10.1007/978-1-4612-1792-3

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1998

  • Hardcover ISBN: 978-0-8176-4026-2Published: 18 December 1998

  • Softcover ISBN: 978-1-4612-7285-4Published: 05 November 2012

  • eBook ISBN: 978-1-4612-1792-3Published: 06 December 2012

  • Edition Number: 2

  • Number of Pages: XI, 244

  • Topics: Group Theory and Generalizations, Field Theory and Polynomials, Algebra

Publish with us

Policies and ethics

Back to top

Search

Navigation