Introduction to Abstract Algebra

Name: Introduction to Abstract Algebra
Availability: InStock
ISBN: 9781118135358

ISBN-10: 1118135350

ISBN-13: 9781118135358

Edition: 4th 2012

Authors: W. Keith Nicholson

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Description:

This Fourth Edition of Introduction to Abstract Algebra is a self-contained introduction to the basic structures of abstract algebra: groups, rings, and fields. This book is intended for a one or two semester abstract algebra course. The writing style is appealing to students, and great effort has been made to motivate and be very clear about how the topics and applications relate to one another. Over 500 solved examples are included to aid reader comprehension as well as to demonstrate how results in the theory are obtained. Many applications (particularly to coding theory, cryptography, and to combinatorics) are provided to illustrate how the abstract structures relate to real-world…

Book details

List price: $275.95
Edition: 4th
Copyright year: 2012
Publisher: John Wiley & Sons, Limited
Publication date: 3/6/2012
Binding: Hardcover
Pages: 560
Size: 7.10" wide x 10.10" long x 1.40" tall
Weight: 2.838
Language: English



Preface


Acknowledgments


Notation 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



Products and Factors



Cauchy's Theorem



Group Actions



The Sylow Theorems



Semidirect Products



An Application to Combinatorics



Series of Subgroups



The Jordan-Hï¿½lder 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 Algebra



Zorn's Lemma



Proof of the Recursion Theorem


Bibliography


Selected Answers


Index