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 Content
1 Groups, Rings and Fields
2 Maximal and Prime Ideals
3 Prime Elements and Unique Factorization Domains
4 Polynomials and Polynomial Rings
5 Field Extensions
6 Field Extensions and Compass and Straightedge Constructions
7 Kronecker’s Theorem and Algebraic Closures
8 Splitting Fields and Normal Extensions
9 Groups, Subgroups and Examples
10 Normal Subgroups, Factor Groups and Direct Products
11 Symmetric and Alternating Groups
12 Solvable Groups
13 Groups Actions and the Sylow Theorems
14 Free Groups and Group Presentations
15 Finite Galois Extensions
16 Separable Field Extensions
17 Applications of Galois Theory
18 The Theory of Modules
19 Finitely Generated Abelian Groups
20 Integral and Transcendental Extensions
21 The Hilbert Basis Theorem and the Nullstellensatz
22 Algebraic Cryptography
About the author
Celine
Carstensen, Volkswohlbund Insurance, Dortmund, Germany;
Benjamin Fine, Fairfield University, Connecticut, USA;
Gerhard Rosenberger, Universität Hamburg, Germany.
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