Introduction to abstract algebra

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Introduction to abstract algebra / W. Keith Nicholson

版:: 4th ed
資料種別:: 図書
出版情報:: Hoboken, N.J. : John Wiley & Sons, c2012
形態:: xxiv, 535 p. ; 27 cm
著者名:: Nicholson, W. Keith <DA07802383>
ISBN:: 9781118135358 [1118135350]
書誌ID:: BB08940871

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注記:

Includes bibliographical references (p. 492-494) and index

主題:

Algebra, Abstract

言語:

英語

目次情報:

Preface

Acknowledgments

Notation Used in The Text

A Sketch of the History of Algebra to 1929

Preliminaries / 0：

Proofs / 0.1：

Sets / 0.2：

Mappings / 0.3：

Equivalences / 0.4：

Integers and Permutations / 1：

Induction / 1.1：

Divisors and Prime Factorization / 1.2：

Integers Modulo n / 1.3：

Permutations / 1.4：

An Application to Cryptography / 1.5：

Groups / 2：

Binary Operations / 2.1：

Subgroups / 2.2：

Cyclic Groups and the Order of an Element / 2.4：

Homomorphisms and Isomorphisms / 2.5：

Cosets and Lagrange's Theorem / 2.6：

Groups of Motions and Symmetries / 2.7：

Normal Subgroups / 2.8：

Factor Groups / 2.9：

The Isomorphism Theorem / 2.10：

An Application to Binary Linear Codes / 2.11：

Rings / 3：

Examples and Basic Properties / 3.1：

Integral Domains and Fields / 3.2：

Ideals and Factor Rings / 3.3：

Homomorphisms / 3.4：

Ordered Integral Domains / 3.5：

Polynomials / 4：

Factorization of Polynomials Over a Field / 4.1：

Factor Rings of Polynomials Over a Field / 4.3：

Partial Fractions / 4.4：

Symmetric Polynomials / 4.5：

Formal Construction of Polynomials / 4.6：

Factorization in Integral Domains / 5：

Irreducibles and Unique Factorization / 5.1：

Principal Ideal Domains / 5.2：

Fields / 6：

Vector Spaces / 6.1：

Algebraic Extensions / 6.2：

Splitting Fields / 6.3：

Finite Fields / 6.4：

Geometric Constructions / 6.5：

The Fundamental Theorem of Algebra / 6.6：

An Application to Cyclic and BCH Codes / 6.7：

Modules over Principal Ideal Domains / 7：

Modules / 7.1：

Modules Over a PID / 7.2：

p-Groups and the Sylow Theorems / 8：

Products and Factors / 8.1：

Cauchy's Theorem / 8.2：

Group Actions / 8.3：

The Sylow Theorems / 8.4：

Semidirect Products / 8.5：

An Application to Combinatorics / 8.6：

Series of Subgroups / 9：

The Jordan-Hölder Theorem / 9.1：

Solvable Groups / 9.2：

Nilpotent Groups / 9.3：

Galois Theory / 10：

Galois Groups and Separability / 10.1：

The Main Theorem of Galois Theory / 10.2：

Insolvability of Polynomials / 10.3：

Cyclotomic Polynomials and Wedderburn's Theorem / 10.4：

Finiteness Conditions for Rings and Modules / 11：

Wedderburn's Theorem / 11.1：

The Wedderburn-Artin Theorem / 11.2：

Appendices

Complex Numbers / Appendix A：

Matrix Algebra / Appendix B：

Zorn's Lemma / Appendix C：

Proof of the Recursion Theorem / Appendix D：

Bibliography

Selected Answers

Index

Preface

Acknowledgments

Notation Used in The Text

A Sketch of the History of Algebra to 1929

Preliminaries / 0：

Proofs / 0.1：

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