First course in abstract algebra : rings, groups, and fields / Marlow Anderson and Todd Feil.

Includes index.

Chapter 1: The Natural Numbers;
Chapter 2: The Integers;
Chapter 3: Modular Arithmetic;
Chapter 4: Polynomials with Rational Coefficients;
Chapter 5: Factorization of Polynomials;
Section I: in a Nutshell;
Part II: Rings, Domains, and Fields;
Chapter 6: Rings;
Chapter 7: Subrings and Unity;
Chapter 8: Integral Domains and Fields;
Chapter 9: Ideals;
Chapter 10: Polynomials over a Field;
Section II: in a Nutshell;
Part III: Ring Homomorphisms and Ideals;
Chapter 11: Ring Homomorphisms;
Chapter 12: The Kernel;
Chapter 13: Rings of Cosets;
Chapter 14: The Isomorphism Theorem for Rings;
Chapter 15: Maximal and Prime Ideals;
Chapter 16: The Chinese Remainder Theorem;
Section III: in a Nutshell;
Part IV: Groups;
Chapter 17: Symmetries of Geometric Figures;
Chapter 18: Permutations;
Chapter 19: Abstract Groups;
Chapter 20: Subgroups;
Chapter 21: Cyclic Groups;
Section IV: in a Nutshell;
Part V: Group Homomorphisms;
Chapter 22: Group Homomorphisms;
Chapter 23: Structure and Representation;
Chapter 24: Cosets and Lagrange's Theorem;
Chapter 25: Groups of Cosets;
Chapter 26: The Isomorphism Theorem for Groups;
Section V: in a Nutshell;
Part VI: Topics from Group Theory;
Chapter 27: The Alternating Groups;
Chapter 28: Sylow Theory: The Preliminaries;
Chapter 29: Sylow Theory: The Theorems;
Chapter 30: Solvable Groups;
Section VI: in a Nutshell;
Part VII: Unique Factorization;
Chapter 31: Quadratic Extensions of the Integers;
Chapter 32: Factorization;
Chapter 33: Unique Factorization;
Chapter 34: Polynomials with Integer Coefficients;
Chapter 35: Euclidean Domains;
Section VII: in a Nutshell;
Part VIII: Constructibility Problems;
Chapter 36: Constructions with Compass and Straightedge;
Chapter 37: Constructibility and Quadratic Field Extensions; Chapter 38: The Impossibility of Certain Constructions;
Section VIII: in a Nutshell;
Part IX: Vector Spaces and Field Extensions;
Chapter 39: Vector Spaces I;
Chapter 40: Vector Spaces II;
Chapter 41: Field Extensions and Kronecker's Theorem; Chapter 42: Algebraic Field Extensions;
Chapter 43: Finite Extensions and Constructibility Revisited; Section IX: in a Nutshell; Part X: Galois Theory;
Chapter 44: The Splitting Field;
Chapter 45: Finite Fields;
Chapter 46: Galois Groups;
Chapter 47: The Fundamental Theorem of Galois Theory;
Chapter 48: Solving Polynomials by Radicals;
Section X: in a Nutshell;
Hints and Solutions;
Guide to Notation;
Indes.

The text includes straightforward exercises within each chapter for students to quickly verify facts, warm-up exercises following the chapter that test fundamental comprehension, and regular exercises concluding the chapter that consist of computational and supply-the-proof problems. Historical remarks discuss the history of algebra to underscore certain pedagogical points. Each section also provides a synopsis that presents important definitions and theorems, allowing students to verify the major topics from the section.