Abstract Algebra, 3rd Edition, is a seminal textbook written by David S. Dummit and Richard M. Foote and published in 2004. The book provides a comprehensive introduction to the subject of abstract algebra, including topics such as group theory, ring theory, field theory, and Galois theory. This textbook is widely used in undergraduate and graduate-level courses and is recognized as one of the most authoritative works in the field of abstract algebra.
One of the key strengths of Abstract Algebra, 3rd Edition, is its clear and concise writing style. The authors do an excellent job of explaining abstract concepts in a way that is accessible to students, making it an ideal choice for those who are new to the subject. The book is well organized, with each chapter building on the material covered in previous chapters, making it easy for students to follow along and understand the material.
In addition to its clear writing style, Abstract Algebra, 3rd Edition, is also notable for its comprehensive coverage of the subject matter. The book covers all of the core topics in abstract algebra, including group theory, ring theory, field theory, and Galois theory, and provides a wealth of examples and exercises to help students understand and apply the concepts.
TABLE OF CONTENTS
Chapter 1 Introduction to Groups
- Basic Axioms and Examples
- Dihedral Groups
- Symmetric Groups
- Matrix Groups
- The Quaternion Group
- Homomorphisms and Isomorphisms
- Group Actions
Chapter 2 Subgroups
- Definition and Examples
- Centralizers and Normalizers, Stabilizers and Kernels
- Cyclic Groups and Cyclic Subgroups
- Subgroups Generated by Subsets of a Group
- The Lattice of Subgroups of a Group
Chapter 3 Quotient Groups and Homomorphisms
- Definitions and Examples
- More on Cosets and Langrange’s Theorem
- The Isomorphism Theorems
- Composition Series and Holder Programme
- Transpositions and the Altering Group
.
Chapter 4 Group Actions
- Group Actions and Permutation Representation
- Groups Acting on Themselves by Left Multiplication-Cayley’s Theorem
- Groups Acting on Themselves by Conjugate-The Class Equation
- Automorphisms
- The Sylow Theorems
- The Simplicity of An
Chapter 5 Direct and Semi-Direct Products and Abelian Groups
- Direct Products
- The Fundamental Theorem of Finitely Generated Abelian Groups
- Table of Groups of Small Order
- Recognizing Direct Products
- Semidirect Products
Chapter 6 Further Topics in Group Theory
- p-Groups, Nilpotent Groups, and Solvable Groups
- Applications in Groups of Medium Order
- A word on Free Groups
Chapter 7 Introduction to Rings
- Basic Definitions and Examples
- Examples: Polynomial Rings, Matrix Rings, and Group Rings
- Ring Homomorphisms and Quotient Rings
- Properties of Ideals
- Rings of Fractions
- The Chinese Remainder Theorem
Chapter 8 Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains
- Euclidean Domains
- Principal Ideal Domains
- Unique Factorization Domains
Chapter 9 Polynomial Rings
- Definitions and Basic Properties
- Polynomial Rings over Fields I
- Polynomial Rings that are Unique Factorization Domains
- Irreducibility Criteria
- Polynomial Rings over Fields II
- Polynomials in Several Variables over a Field and Grobner Bases
Chapter 10 Introduction to Module Theory
- Basic Definitions and Examples
- Quotient Modules and Module Homomorphisms
- Generation of Modules, Direct Sums, and Free Modules
- Tensor Products of Modules
- Exact Sequences-Projective, Injective, and Flat Modules
Chapter 11 Vector Spaces
- Definitions and Basic Theory
- The Matrix of a Linear Transformation
- Dual Vector Spaces
- Determinants
- Tensor Algebras, Symmetric and Exterior Algebras
Chapter 12 Modules over Principal Ideal Domains
- The Basic Theory
- The Rational Canonical Form
- The Jordan Canonical Form
Chapter 13 Basic Theory of Field Extensions
- Algebraic Extensions
- Classical Straightedge and Compass Constructions
- Splitting Fields and Algebraic Closures
- Separable and Inseparable Extensions
- Cyclotomic Polynomials and Extensions
Chapter 14 Galois Theory
- Basic Definitions
- The Fundamental Theorem of Galois Theory
- Finite Fields
- Composite Extensions and Simple Extensions
- Cyclotomic Extensions and Abelian Extensions over Q
- Galois Groups of Polynomials
- Solvable and Radical Extensions: Insolvability of the Quintic
- Computation of Galois Groups over Q
- Transcendental Extensions, Inseparable Extensions, Infinite Galois Groups
Chapter 15 Commutative Rings and Algebraic Geometry
- Noetherian Rings and Affine Algebraic Sets
- Radicals and Affine Varieties
- Integral Extensions and Hilbert’s Nullstellensatz
- Localization
- The Prime Spectrum of a Ring
Chapter 16 Artinian Rings, Discrete Valuation Rings, and Dedekind Domains
- Artinian Rings
- Discrete Valuation Rings
- Dedekind Domains
Chapter 17 Introduction to Homological Algebra and Group Cohomology
- Introduction to Homological Algebra-Ext and Tor
- The Cohomology of Groups
- Crossed Homomorphisms and H1(G, A)
- Group Extensions, factor Sets and H2(G,A)
Chapter 18 Representation Theory and Character Theory
- Linear Actions and Modules over Group Rings
- Wedderburn’s Theorem and Some Consequences
- Character Theory and the Orthogonality Relations
Chapter 19 Examples and Applications of Character Theory
- Characters of Groups of Small Order
- Theorems of Burnside and Hall
- Introduction to the Theory of Induced Characters
Download Now Book in PDF
The book is also designed to be flexible and can be used in a variety of different courses and settings. Whether you are studying abstract algebra in a traditional classroom setting or working through the material on your own, Abstract Algebra, 3rd Edition, is an excellent resource that will provide you with a solid foundation in the subject.
For those looking to further their understanding of abstract algebra, Abstract Algebra, 3rd Edition, is an excellent choice. Whether you are a student, a teacher, or just someone who is interested in the subject, this book provides a comprehensive and accessible introduction to abstract algebra.
And the good news is, we have this book in PDF format to download, so you can access it anytime and anywhere. The PDF format allows you to easily search the book, highlight key passages, and take notes, making it a convenient and accessible resource for students of all levels.
In conclusion, Abstract Algebra, 3rd Edition, is a comprehensive and accessible textbook that is ideal for students and teachers of abstract algebra. Its clear writing style, comprehensive coverage of the subject matter, and flexible design make it a valuable resource for anyone looking to deepen their understanding of abstract algebra.
