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1 Beaverton Mathematics- Algebra

Elements of Abstract Algebra

by

Elements of Abstract Algebra Cover

 

Synopses & Reviews

Publisher Comments:

This concise, readable, college-level text treats basic abstract algebra in remarkable depth and detail. An antidote to the usual surveys of structure, the book presents group theory, Galois theory, and classical ideal theory in a framework emphasizing proof of important theorems.

Chapter I (Set Theory) covers the basics of sets. Chapter II (Group Theory) is a rigorous introduction to groups. It contains all the results needed for Galois theory as well as the Sylow theorems, the Jordan-Holder theorem, and a complete treatment of the simplicity of alternating groups. Chapter III (Field Theory) reviews linear algebra and introduces fields as a prelude to Galois theory. In addition there is a full discussion of the constructibility of regular polygons. Chapter IV (Galois Theory) gives a thorough treatment of this classical topic, including a detailed presentation of the solvability of equations in radicals that actually includes solutions of equations of degree 3 and 4 ― a feature omitted from all texts of the last 40 years. Chapter V (Ring Theory) contains basic information about rings and unique factorization to set the stage for classical ideal theory. Chapter VI (Classical Ideal Theory) ends with an elementary proof of the Fundamental Theorem of Algebraic Number Theory for the special case of Galois extensions of the rational field, a result which brings together all the major themes of the book.

The writing is clear and careful throughout, and includes many historical notes. Mathematical proof is emphasized. The text comprises 198 articles ranging in length from a paragraph to a page or two, pitched at a level that encourages careful reading. Most articles are accompanied by exercises, varying in level from the simple to the difficult.

Synopsis:

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.

Synopsis:

Helpful illustrations and exercises included throughout this lucid coverage of group theory, Galois theory and classical ideal theory stressing proof of important theorems. Includes many historical notes. Mathematical proof is emphasized. Includes 24 tables and figures. Reprint of the 1971 edition.

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

Product Details

ISBN:
9780486647258
Author:
Clark, Allan
Publisher:
Dover Publications
Author:
Mathematics
Location:
New York :
Subject:
Mathematics
Subject:
Algebra
Subject:
Algebra - General
Subject:
Algebra - Abstract
Subject:
General Mathematics
Subject:
Mathematics - Algebra
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
no. 47 (May 1981)
Publication Date:
19841031
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
224
Dimensions:
8.5 x 5.38 in 0.56 lb

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Related Subjects

Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Algebra » General

Elements of Abstract Algebra Used Trade Paper
0 stars - 0 reviews
$6.50 In Stock
Product details 224 pages Dover Publications - English 9780486647258 Reviews:
"Synopsis" by ,
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.

"Synopsis" by ,
Helpful illustrations and exercises included throughout this lucid coverage of group theory, Galois theory and classical ideal theory stressing proof of important theorems. Includes many historical notes. Mathematical proof is emphasized. Includes 24 tables and figures. Reprint of the 1971 edition.
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