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Abstract Algebra : Applications to Galois Theory, Algebraic Geometry and Cryptography - Gerhard Rosenberger

Abstract Algebra

Applications to Galois Theory, Algebraic Geometry and Cryptography

Hardcover Published: 28th January 2011
ISBN: 9783110250084
Number Of Pages: 366
For Ages: 18+ years old

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?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.

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.

ISBN: 9783110250084
ISBN-10: 311025008X
Series: SIGMA Series in Pure Mathematics
Audience: General
For Ages: 18+ years old
For Grades: 13 - 16
Format: Hardcover
Language: English
Number Of Pages: 366
Published: 28th January 2011
Country of Publication: DE
Dimensions (cm): 23.88 x 17.02  x 2.03
Weight (kg): 0.64