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First Course in Abstract Algebra, A, 8th edition

  • John B Fraleigh, 
  • Neal Brand

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Overview

A First Course in Abstract Algebra is an in-depth introduction ideal for future graduate students, future high school teachers, and students who intend to work in industry.  


Published by Pearson (May 1st 2020) - Copyright © 2021

ISBN-13: 9780135859759

Subject: Advanced Math

Category: Abstract Algebra

Table of contents

Brief Table of Contents

  • Instructor's Preface
  • Dependence Chart
  • Student's Preface
  1. Sets and Relations

I. GROUPS AND SUBGROUPS

  1. Binary Operations
  2. Groups
  3. Abelian Groups
  4. Nonabelian Examples
  5. Subgroups
  6. Cyclic Groups
  7. Generating Sets and Cayley Digraphs

II. STRUCTURE OF GROUPS

  1. Groups and Permutations
  2. Finitely Generated Abelian Groups
  3. Cosets and the Theorem of Lagrange
  4. Plane Isometries

III. HOMOMORPHISMS AND FACTOR GROUPS

  1. Factor Groups
  2. Factor-Group Computations and Simple Groups
  3. Groups Actions on a Set
  4. Applications of G -Sets to Counting

IV. ADVANCED GROUP THEORY

  1. Isomorphism Theorems
  2. Sylow Theorems
  3. Series of Groups
  4. Free Abelian Groups
  5. Free Groups
  6. Group Presentations

V. RINGS AND FIELDS

  1. Rings and Fields
  2. Integral Domains
  3. Fermat's and Euler's Theorems
  4. Encryption

VI. CONSTRUCTING RINGS AND FIELDS

  1. The Field of Quotients of an Integral Domain
  2. Rings and Polynomials
  3. Factorization of Polynomials over Fields
  4. Algebraic Coding Theory
  5. Homomorphisms and Factor Rings
  6. Prime and Maximal Ideals
  7. Noncommutative Examples

VII. COMMUTATIVE ALGEBRA

  1. Vector Spaces
  2. Unique Factorization Domains
  3. Euclidean Domains
  4. Number Theory
  5. Algebraic Geometry
  6. Gröbner Basis for Ideals

VIII. EXTENSION FIELDS

  1. Introduction to Extension Fields
  2. Algebraic Extensions
  3. Geometric Constructions
  4. Finite Fields

IX. Galois Theory

  1. Introduction to Galois Theory
  2. Splitting Fields
  3. Separable Extensions
  4. Galois Theory
  5. Illustrations of Galois Theory
  6. Cyclotomic Extensions
  7. Insolvability of the Quintic

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