Elements of Abstract Algebra

Elements of Abstract Algebra

by Allan Clark
     
 


Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.
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Overview


Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.

Product Details

ISBN-13:
9780486647258
Publisher:
Dover Publications
Publication date:
10/01/1984
Series:
Dover Books on Mathematics Series
Pages:
224
Sales rank:
592,100
Product dimensions:
5.50(w) x 8.40(h) x 0.50(d)

Related Subjects

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

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