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Introduction to Abstract Algebra

ISBN-10: 0471331090

ISBN-13: 9780471331094

Edition: 2nd 1999 (Revised)

Authors: W. Keith Nicholson

List price: $125.00
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Description:

Clearly written and self-contained, this new edition of a successful book features precise, careful explanations of advanced algebra concepts such as groups, semi-groups, rings, modules, fields, and similar structures. It then goes a step farther and presents interesting motivational applications of algebraic ideas to cryptography, coding theory, etc.
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Book details

List price: $125.00
Edition: 2nd
Copyright year: 1999
Publisher: John Wiley & Sons, Incorporated
Publication date: 7/23/1999
Binding: Hardcover
Pages: 624
Size: 6.25" wide x 9.25" long x 1.50" tall
Weight: 2.134
Language: English

Preface
Acknowledgment
Notations Used in the Text
A Sketch of the History of Algebra to 1929
Preliminaries
Proofs
Sets
Mappings
Equivalences
Integers and Permutations
Induction
Divisors and Prime Factorization
Integers Modulo n
Permutations
An Application to Cryptography
Groups
Binary Operations
Groups
Subgroups
Cyclic Groups and the Order of an Element
Homomorphisms and Isomorphisms
Cosets and Lagrange's Theorem
Groups of Motions and Symmetries
Normal Subgroups
Factor Groups
The Isomorphism Theorem
An Application to Binary Linear Codes
Rings
Examples and Basic Properties
Integral Domains and Fields
Ideals and Factor Rings
Homomorphisms
Ordered Integral Domains
Polynomials
Polynomials
Factorization of Polynomials over a Field
Factor Rings of Polynomials over a Field
Partial Fractions
Symmetric Polynomials
Formal Construction of Polynomials
Factorization in Integral Domains
Irreducibles and Unique Factorization
Principal Ideal Domains
Fields
Vector Spaces
Algebraic Extensions
Splitting Fields
Finite Fields
Geometric Constructions
The Fundamental Theorem of Algebra
An Application to Cyclic and BCH Codes
Modules over Principal Ideal Domains
Modules
Modules over a PID
p-Groups and the Sylow Theorems
Factors and Products
Cauchy's Theorem
Group Actions
The Sylow Theorems
Semidirect Products
An Application to Combinatorics
Series of Subgroups
The Jordan-Holder Theorem
Solvable Groups
Nilpotent Groups
Galois Theory
Galois Groups and Separability
The Main Theorem of Galois Theory
Insolvability of Polynomials
Cyclotomic Polynomials and Wedderburn's Theorem
Finiteness Conditions for Rings and Modules
Wedderburn's Theorem
The Wedderburn-Artin Theorem
Appendices
Complex Numbers
Matrix Arithmetic
Zorn's Lemma
Proof of the Recursion Theorem
Bibliography
Selected Answers
Index