eBook - ePub
Abstract Algebra
With Applications to Galois Theory, Algebraic Geometry, Representation Theory and Cryptography
- 422 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
Abstract Algebra
With Applications to Galois Theory, Algebraic Geometry, Representation Theory and Cryptography
About this book
Abstract algebra is the study of algebraic structures like groups, rings and fields. This book provides an account of the theoretical foundations including applications to Galois Theory, Algebraic Geometry and Representation Theory. It implements the pedagogic approach to conveying algebra from the perspective of rings. The 3 rd edition provides a revised and extended versions of the chapters on Algebraic Cryptography and Geometric Group Theory.
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Yes, you can access Abstract Algebra by Gerhard Rosenberger,Annika Schürenberg,Leonard Wienke in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebra. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- Title Page
- Copyright
- Contents
- 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 Group 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 Algebras and Group Representations
- 23 Algebraic Cryptography
- 24 Non-Commutative Group Based Cryptography
- Subject Index