Book:Richard A. Dean/Elements of Abstract Algebra
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Richard A. Dean: Elements of Abstract Algebra
Published $\text {1966}$, Wiley International Edition
- ISBN 0 471 20452 8
Subject Matter
- Abstract Algebra
- Group Theory
- Field Theory
- Euclidean Domains
- Polynomial Theory
- Vector Spaces
- Galois Theory
Contents
- Preface
- Chapter 0
- 0.1 Arithmetic
- 0.2 Sets
- 0.3 Relations
- 0.4 Functions and Mappings
- 0.5 Operations and Operators
- 0.6 Combinatorics
- Prologue
- Chapter 1: Groups
- 1.1 Introduction
- 1.2 Group Axioms
- 1.3 Examples
- 1.4 Basic Lemmas
- 1.5 Isomorphism
- 1.6 Permutation Groups
- 1.7 Cyclic Groups
- 1.8 Dihedral Groups
- 1.9 Subgroups
- 1.10 Homomorphisms
- 1.11 Direct Products
- Chapter 2: Rings
- 2.1 Definitions
- 2.2 Basic Lemmas
- 2.3 Subrings
- 2.4 Homomorphisms
- 2.5 Integral Domains
- Chapter 3: The Integers
- 3.1 Introduction
- 3.2 Order
- 3.3 Order in Integral Domains
- 3.4 Well-Ordered Sets
- 3.5 The Integers
- 3.6 Arithmetic in the Integers
- Chapter 4: Fields
- 4.1 Introduction
- 4.2 Field of Quotients
- 4.3 Subfields
- 4.4 Homomorphism of Fields
- 4.5 The Real Numbers
- 4.6 The Complex Numbers
- Chapter 5: Euclidean Domains
- 5.1 Introduction
- 5.2 The Euclidean Algorithm
- 5.3 Arithmetic in Euclidean Domains
- 5.4 Application to Groups
- Chapter 6: Polynomials
- 6.1 Introduction
- 6.2 Polynomial Rings
- 6.3 Polynomials Over a Field
- 6.4 The Complex Numbers
- 6.5 Special Properties of $F \sqbrk x$
- 6.6 Factorization in $R \sqbrk x$
- 6.7 Field of Quotients of $R \sqbrk x$
- 6.8 Polynomials in Several Variables
- Chapter 7: Vector Spaces
- 7.1 Introduction
- 7.2 Definition and Examples
- 7.3 Subspaces
- 7.4 Dependence and Basis
- 7.5 Linear Transformations
- 7.6 Solutions of Systems of Linear Equations
- 7.7 Algebras
- Chapter 8: Field Extensions and Finite Fields
- 8.1 Construction of Field Extensions
- 8.2 Classification of Extensions
- 8.3 Transcendental Extensions
- 8.4 Algebraic Extensions
- 8.5 Finite Fields
- 8.6 Simple Extensions
- 8.7 Roots of Unity
- 8.8 Wedderburn's Theorem
- Chapter 9: Finite Groups
- 9.1 Cauchy's Theorem
- 9.2 $p$-Groups
- 9.3 The Sylow Theorems
- 9.4 Solvable Groups
- 9.5 Abelian Groups
- Chapter 10: Galois Theory
- 10.1 Fundamental Theorem of Galois Theory
- 10.2 Cyclotomic Fields and Cyclic Extensions
- 10.3 Solution of Equations by Radicals
- 10.4 Equations of 2nd and 3rd Degree
- 10.5 The General Polynomial of $n$th Degree
- 10.6 The Discriminant
- 10.7 Symmetric Polynomials
- Answers to Exercises
- Symbols and Notations
- Index
Source work progress
- 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 1.10$: Theorem $31$
- Exercises not done. Redoing from start.
- 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 0.3$. Relations
- Go through it again because the examples are not all done.