Galois Theory Through Exercises

• Main Author: Brzeziński, Juliusz (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 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.; Field Theory and Polynomials.; Number Theory.; Algebraic Geometry.; Associative Rings and Algebras.; Commutative Rings and Algebras.; Group Theory and Generalizations.

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...

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.