Abstract Algebra Applications to Galois Theory Algebraic Geometry and Cryptography 1st Edition by Celine Carstensen, Benjamin Fine, Gerhard Rosenberger 9783110250084 311025008X
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Product details:
ISBN 10: 311025008X
ISBN 13: 9783110250084
Author: Celine Carstensen, Benjamin Fine, Gerhard Rosenberger
A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theoretical foundations; also contains topics that cannot be found elsewhere, and also offers a chapter on cryptography. End of chapter problems help readers with accessing the subjects. This work is co-published with the Heldermann Verlag, and within Heldermann’s Sigma Series in Mathematics.
Table of contents:
Chapter 1: Groups, Rings and Fields
Chapter 2: Maximal and Prime Ideals
Chapter 3: Prime Elements and Unique Factorization Domains
Chapter 4: Polynomials and Polynomial Rings
Chapter 5: Field Extensions
Chapter 6: Field Extensions and Compass and Straightedge Constructions
Chapter 7: Kronecker’s Theorem and Algebraic Closures
Chapter 8: Splitting Fields and Normal Extensions
Chapter 9: Groups, Subgroups and Examples
Chapter 10: Normal Subgroups, Factor Groups and Direct Products
Chapter 11: Symmetric and Alternating Groups
Chapter 12: Solvable Groups
Chapter 13: Groups Actions and the Sylow Theorems
Chapter 14: Free Groups and Group Presentations
Chapter 15: Finite Galois Extensions
Chapter 16: Separable Field Extensions
Chapter 17: Applications of Galois Theory
Chapter 18: The Theory of Modules
Chapter 19: Finitely Generated Abelian Groups
Chapter 20: Integral and Transcendental Extensions
Chapter 21: The Hilbert Basis Theorem and the Nullstellensatz
Chapter 22: Algebraic Cryptography
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Tags: Celine Carstensen, Benjamin Fine, Gerhard Rosenberger, Abstract