Abstract Algebra: Applications to Galois Theory, Algebraic Geometry and Cryptography by Gerhard Rosenberger & Benjamin Fine & Celine Carstensen
Contents of Abstract Algebra
- Groups, Rings and Fields
- Maximal and Prime Ideals
- Prime Elements and Unique Factorization Domains
- Polynomials and Polynomial Rings
- Field Extensions
- Field Extensions and Compass and Straightedge Constructions
- Kronecker’s Theorem and Algebraic Closures
- Splitting Fields and Normal Extensions
- Groups, Subgroups and Examples
- Normal Subgroups, Factor Groups and Direct Products
- Symmetric and Alternating Groups
- Solvable Groups
- Groups Actions and the Sylow Theorems
- Free Groups and Group Presentations
- Finite Galois Extensions
- Separable Field Extensions
- Applications of Galois Theory
- The Theory of Modules
- Finitely Generated Abelian Groups
- Integral and Transcendental Extensions
- The Hilbert Basis Theorem and the Nullstellensatz
- Algebraic Cryptography
