Table of Contents

Foreword; Introduction I. Set Theory 1-9. The notation and terminology of set theory 10-16. Mappings 17-19. Equivalence relations 20-25. Properties of natural numbers II. Group Theory 26-29. Definition of group structure 30-34. Examples of group structure 35-44. Subgroups and cosets 45-52. Conjugacy, normal subgroups, and quotient groups 53-59. The Sylow theorems 60-70. Group homomorphism and isomorphism 71-75. Normal and composition series 76-86. The Symmetric groups III. Field Theory 87-89. Definition and examples of field structure 90-95. Vector spaces, bases, and dimension 96-97. Extension fields 98-107. Polynomials 108-114. Algebraic extensions 115-121. Constructions with straightedge and compass IV. Galois Theory 122-126. Automorphisms 127-138. Galois extensions 139-149. Solvability of equations by radicals V. Ring Theory 150-156. Definition and examples of ring structure 157-168. Ideals 169-175. Unique factorization VI. Classical Ideal Theory 176-179. Fields of fractions 180-187. Dedekind domains 188-191. Integral extensions 192-198. Algebraic integers Bibliography; Index