An Introduction to Abstract Algebra / Edition 2

by F. M. Hall

Overview

The second volume continues the course of study started in Volume 1, but may be used independently by those already possessing an elementary knowledge of the subject. A summary of basic group theory is followed by accounts of group homomorphisms, rings, fields and integral domains. The related concepts of an invariant subgroup and an ideal in a ring are brought in and the reader introduced to vector spaces and Boolean algebra. The theorems behind the abstract work and the reasons for their importance are discussed in greater detail than is usual at this level. The book is intended both for those who, educated in traditional mathematics, wish to know something about modern algebra and also for those already familiar with the elements of the subject who wish to study further. Fresh ideas and structures are introduced gradually and in a simpler manner, with concrete examples and much more informal discussion. There are many graded exercises, including some worked examples. This book is thus suitable both for the student working by himself without the aid of the teacher and for those taking formal courses in universities or colleges of education.

Product Details

ISBN-13:	9780521298629
Publisher:	Cambridge University Press
Publication date:	02/14/1980
Edition description:	Revised ed.
Pages:	404
Product dimensions:	5.50(w) x 8.50(h) x 1.10(d)

Table of Contents

Preface; 1. Introduction; 2. Sets; 3. Elementary set theory; 4. The set of integers; 5. Other sets of numbers; 6. Residue classes; 7. Polynomials; 8. Vectors; 9. Functions and mappings; 10. The fundamental laws of algebra; 11. Groups; 12. Examples of groups; 13. Subgroups; Answers to exercises; Index.