A First Course in Abstract Algebra: Rings, Groups, and Fields, Third Edition (Hardcover, 3)

Numbers, Polynomials, and Factoring
The Natural Numbers
The Integers
Modular Arithmetic
Polynomials with Rational Coefficients
Factorization of Polynomials
Section I in a Nutshell

Rings, Domains, and Fields
Rings
Subrings and Unity
Integral Domains and Fields
Ideals
Polynomials over a Field
Section II in a Nutshell

Ring Homomorphisms and Ideals
Ring Homomorphisms
The Kernel
Rings of Cosets
The Isomorphism Theorem for Rings
Maximal and Prime Ideals
The Chinese Remainder Theorem
Section III in a Nutshell

Groups
Symmetries of Geometric Figures
Permutations
Abstract Groups
Subgroups
Cyclic Groups
Section IV in a Nutshell

Group Homomorphisms
Group Homomorphisms
Structure and Representation
Cosets and Lagrange's Theorem
Groups of Cosets
The Isomorphism Theorem for Groups
Section V in a Nutshell

Topics from Group Theory
The Alternating Groups
Sylow Theory: The Preliminaries
Sylow Theory: The Theorems
Solvable Groups
Section VI in a Nutshell

Unique Factorization
Quadratic Extensions of the Integers
Factorization
Unique Factorization
Polynomials with Integer Coefficients
Euclidean Domains
Section VII in a Nutshell

Constructibility Problems
Constructions with Compass and Straightedge
Constructibility and Quadratic Field Extensions
The Impossibility of Certain Constructions
Section VIII in a Nutshell

Vector Spaces and Field Extensions
Vector Spaces I
Vector Spaces II
Field Extensions and Kronecker's Theorem
Algebraic Field Extensions
Finite Extensions and Constructibility Revisited
Section IX in a Nutshell

Galois Theory
The Splitting Field
Finite Fields
Galois Groups
The Fundamental Theorem of Galois Theory
Solving Polynomials by Radicals
Section X in a Nutshell