A First Course in Abstract Algebra: Rings, Groups, and Fields

Content: Front Cover
 Contents
 Preface
 Part I: Numbers, Polynomials, and Factoring
 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 CosetsChapter 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 GroupsSection 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 StraightedgeChapter 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 TheoryChapter 48: Solving Polynomials by Radicals
 Section X: in a Nutshell
 Hints and Solutions
 Guide to Notation.