Abstract Algebra : : Applications to Galois Theory, Algebraic Geometry and Cryptography / / Gerhard Rosenberger, Benjamin Fine, Celine Carstensen.

• Superior document: Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1
• VerfasserIn: Carstensen, Celine,; Fine, Benjamin,; Rosenberger, Gerhard,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2011]; ©2011
• Year of Publication: 2011
• Language: English
• Series: De Gruyter Textbook
• Physical Description: 1 online resource (366 p.) :; Num. figs.

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

Frontmatter -- Preface -- 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 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 -- Bibliography -- Index