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Abstract Algebra
Applications to Galois Theory, Algebraic Geometry and Cryptography
-
Celine Carstensen
Language:
English
Published/Copyright:
2011
About this book
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.
- Providing an accessible account of the theoretical foundations
- Covering topics not found in competing works: Free groups, module theory, extensions of rings
- Also including cryptography
- Comes with end of chapter problems
Author / Editor information
Celine Carstensen, Volkswohlbund Insurance, Dortmund, Germany; Benjamin Fine, Fairfield University, Connecticut, USA; Gerhard Rosenberger, Universität Hamburg, Germany.
Topics
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Frontmatter
I -
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Preface
V -
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Contents
VII -
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1 Groups, Rings and Fields
1 -
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2 Maximal and Prime Ideals
21 -
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3 Prime Elements and Unique Factorization Domains
29 -
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4 Polynomials and Polynomial Rings
53 -
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5 Field Extensions
66 -
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6 Field Extensions and Compass and Straightedge Constructions
80 -
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7 Kronecker’s Theorem and Algebraic Closures
91 -
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8 Splitting Fields and Normal Extensions
113 -
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9 Groups, Subgroups and Examples
119 -
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10 Normal Subgroups, Factor Groups and Direct Products
141 -
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11 Symmetric and Alternating Groups
161 -
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12 Solvable Groups
171 -
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13 Groups Actions and the Sylow Theorems
180 -
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14 Free Groups and Group Presentations
192 -
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15 Finite Galois Extensions
217 -
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16 Separable Field Extensions
233 -
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17 Applications of Galois Theory
248 -
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18 The Theory of Modules
265 -
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19 Finitely Generated Abelian Groups
285 -
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20 Integral and Transcendental Extensions
295 -
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21 The Hilbert Basis Theorem and the Nullstellensatz
312 -
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22 Algebraic Cryptography
326 -
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Bibliography
359 -
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Index
363
Publishing information
Pages and Images/Illustrations in book
eBook published on:
February 28, 2011
eBook ISBN:
9783110250091
Pages and Images/Illustrations in book
Front matter:
11
Main content:
366
Other:
Num. figs.
eBook ISBN:
9783110250091
Audience(s) for this book
Advanced Students, Mathematicians, Theoretical Physicists, Cryptologists; Academic Libraries
