Galois Theory Through Exercises / / by Juliusz Brzeziński

• Autore: Brzeziński Juliusz
• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018
• Edizione: 1st ed. 2018.
• Descrizione fisica: 1 online resource (XVII, 293 p. 12 illus.)
• Disciplina: 512.32
• Soggetto topico: 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
• Nota di contenuto: 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.
• Sommario/riassunto: 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’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading. A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study.
• Titolo autorizzato: Galois Theory Through Exercises
• ISBN: 3-319-72326-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910300102903321
• Lo trovi qui: Univ. Federico II
• Serie: Springer Undergraduate Mathematics Series, . 1615-2085