Introduction to the Galois Correspondence - Softcover

Inhaltsangabe

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. Wedderburn's Theorem.- 3. Dirichlet's 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.

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