Author | Fenrick, Maureen H. author |
---|---|
Title | Introduction to the Galois Correspondence [electronic resource] / by Maureen H. Fenrick |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1998 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1792-3 |
Descript | XI, 244 p. online resource |
I. Preliminaries - Groups and Rings -- 1. Introduction to Groups -- 2. Quotient Groups and Sylow Subgroups -- 3. Finite Abelian Groups and Solvable Groups -- 4. Introduction to Rings -- 5. Factoring in F[x] -- II. Field Extensions -- 1. Simple Extensions -- 2. Algebraic Extensions -- 3. Splitting Fields and Normal Extensions -- III. The Galois Correspondence -- 1. The Fundamental Correspondence -- 2. The Solvable Correspondence -- IV. Applications -- 1. Constructibility -- 2. Roots of Unity -- 3. Wedderburnโs Theorem -- 3. Dirichletโs Theorem and Finite Abelian Groups -- Appendix A - Groups -- 1. Group Actions and the Sylow Theorems -- 2. Free Groups, Generators and Relations -- Appendix B - Factoring in Integral Domains -- 1. Euclidean Domains and Principal Ideal Domains -- 2. Prime and Irreducible Elements -- 3. Unique Factorization Domains -- Appendix C - Vector Spaces -- 1. Subspaces, Linear Independence and Spanning -- 2. Bases and Dimension