Introduction to Abstract Algebra

Name: Introduction to Abstract Algebra
Availability: OutOfStock
ISBN: 9780471331094

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.

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