Galois Theory Through Exercises

This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois' the...

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Bibliographic Details
Main Author: Brzeziński, Juliusz (Author)
Format: Electronic eBook
Language:English
Published: Cham : Springer International Publishing, 2018.
Edition:1st ed. 2018.
Series:Springer Undergraduate Mathematics Series,
Subjects:
Algebra.
Field theory (Physics).
Number theory.
Algebraic geometry.
Associative rings.
Rings (Algebra).
Commutative algebra.
Commutative rings.
Group theory.
ISBN:9783319723266
ISSN:1615-2085
Online Access: Get full text
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Table of Contents:
  • 1 Solving algebraic equations
  • 2 Field extensions
  • 3 Polynomials and irreducibility
  • 4 Algebraic extensions
  • 5 Splitting fields
  • 6 Automorphism groups of fields
  • 7 Normal extensions
  • 8 Separable extensions
  • 9 Galois extensions
  • 10 Cyclotomic extensions
  • 11 Galois modules
  • 12 Solvable groups
  • 13 Solvability of equations
  • 14 Geometric constructions
  • 15 Computing Galois groups
  • 16 Supplementary problems
  • 17 Proofs of the theorems
  • 18 Hints and answers
  • 19 Examples and selected solutions
  • Appendix: Groups, rings and fields
  • References
  • List of notations
  • Index.

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