Galois Theory / Edition 2

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Overview

A clear, efficient exposition of this topic with complete proofs and exercises, covering cubic and quartic formulas; fundamental theory of Galois theory; insolvability of the quintic; Galoiss Great Theorem; and computation of Galois groups of cubics and quartics. Suitable for first-year graduate students, either as a text for a course or for study outside the classroom, this new edition has been completely rewritten in an attempt to make proofs clearer by providing more details. It now begins with a short section on symmetry groups of polygons in the plane, for there is an analogy between polygons and their symmetry groups and polynomials and their Galois groups - an analogy which serves to help readers organise the various field theoretic definitions and constructions. The text is rounded off by appendices on group theory, ruler-compass constructions, and the early history of Galois Theory. The exposition has been redesigned so that the discussion of solvability by radicals now appears later and several new theorems not found in the first edition are included.

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Editorial Reviews

Booknews
An introductory textbook for first year graduate students with a knowledge of both linear and abstract algebra. Includes complete proofs, exercises, and a history of the 19th century theory. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780387985411
  • Publisher: Springer New York
  • Publication date: 9/1/2001
  • Series: Universitext Series
  • Edition description: 2nd ed. 1998. Corr. 2nd printing 2001
  • Edition number: 2
  • Pages: 190
  • Product dimensions: 0.38 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Symmetry. Rings. Domains and Fields. Homomorphisms and Ideals. Quotient Rings. Polynomial Rings over Fields. Prime Ideals and Maximal Ideals. Irreducible Polynomials. Classical Formulas. Splitting Fields. The Galois Group. Roots of Unity. Solvability by Radicals. Independence of Characters. Galois Extensions. The Fundamental Theorem of Galois Theory. Applications. Galois's Great Theorem. Discriminants. Galois Groups of Quadratics, Dubics, and Quartics. Epilogue. Appendices.

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