---

＜電子ブック＞
Galois Theory Through Exercises / by Juliusz Brzeziński
(Springer Undergraduate Mathematics Series. ISSN:21974144)

版	1st ed. 2018.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2018
大きさ	XVII, 293 p. 12 illus : online resource
著者標目	*Brzeziński, Juliusz author SpringerLink (Online service)
件　名	LCSH:Algebraic fields LCSH:Polynomials LCSH:Number theory LCSH:Algebraic geometry LCSH:Associative rings LCSH:Associative algebras LCSH:Commutative algebra LCSH:Commutative rings LCSH:Group theory FREE:Field Theory and Polynomials FREE:Number Theory FREE:Algebraic Geometry FREE:Associative Rings and Algebras FREE:Commutative Rings and Algebras FREE:Group Theory and Generalizations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-72326-6

 類似資料