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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

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

Library of Congress subject headings for this publication: Algebra, Abstract