An Introductory Course in Commutative Algebra

by Chatters, A. W.; Hajarnavis, C. R.

• ISBN13: 9780198501442
• ISBN10: 0198501447
• Format: Paperback
• Copyright: 1998-07-16
• Publisher: Clarendon Press

Summary

This book aims to be a concise introduction to topics in commutative algebra, with an emphasis on worked examples and applications. It combines elegant algebraic theory with applications to number theory, problems in classical Greek geometry, and the theory of finite fields which hasimportant uses in other branches of science. Topics covered include rings and Euclidean rings, the four-squares theorem, fields and field extensions, finite cyclic groups and finite fields. The material covered in this book prepares the way for the further study of abstract algebra, but it couldalso form the basis of an entire course.

Table of Contents

Rings

Euclidean rings

Highest common factor

The four-squares theorem

Fields and polynomials

Unique factorization domains

Field of quotients of an integral domain

Factorization of polynomials

Fields and field extensions

Finite cyclic groups and finite fields

Algebraic numbers

Ruler and Compass constructions

Homomorphisms, ideals and factor rings

Principal ideal domains and a method for constructing fields

Finite fields

Solutions to selected exercises

References

Table of Contents provided by Publisher. All Rights Reserved.