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Classical Galois Theory with Examples
Lisl Gaal, University of Minnesota, Minneapolis, MN

AMS Chelsea Publishing
1971; 248 pp; hardcover
Volume: 268
Reprint/Revision History:
first AMS printing 1998
ISBN-10: 0-8218-1375-7
ISBN-13: 978-0-8218-1375-1
List Price: US$38
Member Price: US$34.20
Order Code: CHEL/268.H
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"This book is strongly recommended to beginning graduate students who already have some background in abstract algebra. The exposition and proofs are intended to present Galois theory in as simple a manner as possible ... The large number of partially or fully solved examples is its special feature."

-- Mathematical Reviews

"Excellent for undergraduate independent study since it demands reader participation."

-- American Mathematical Monthly

Table of Contents

  • Prerequisites: 1.1 Group theory; 1.2 Permutations and permutation groups; 1.3 Fields; 1.4 Rings and polynomials; 1.5 Some elementary theory of equations; 1.6 Vector spaces
  • Fields: 2.1 Degree of an algebraic extension; 2.2 Isomorphisms of fields; 2.3 Automorphisms of fields; 2.4 Fixed fields
  • Fundamental theorem: 3.1 Splitting fields; 3.2 Normal extensions and groups of automorphisms; 3.3 Conjugate fields and elements; 3.4 Fundamental theorem
  • Applications: 4.1 Solvability of equations; 4.2 Solvable equations have solvable groups; 4.3 General equation of degree \(n\); 4.4 Roots of unity and cyclic equations; 4.5 How to solve a solvable equation; 4.6 Ruler-and-compass constructions; 4.7 Lagrange's theorem; 4.8 Resolvent of a polynomial; 4.9 Calculation of the Galois group; 4.10 Matrix solutions of equations; 4.11 Finite fields; 4.12 More applications
  • Bibliography
  • Index
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