Synopses & Reviews
In this well-written introduction to commutative algebra, the author shows the link between commutative ring theory and algebraic geometry. In addition to standard material, the book contrasts the methods and ideology of modern abstract algebra with concrete applications in algebraic geometry and number theory. Professor Reid begins with a discussion of modules and Noetherian rings before moving on to finite extensions and the Noether normalization. Sections on the nullstellensatz and rings of fractions precede sections on primary decomposition and normal integral domains. This book is ideal for anyone seeking a primer on commutative algebra.
Review
'It gives a fresh picture of the subject for a new generation of students.' P. Scnezel, Zentralblatt fur Mathematik
Review
'The author takes care to explain the geometric and number theoretic meaning of the algebraic methods and results presented. This makes the book perhaps more demanding, but surely much more interesting than the standard ones.' European Mathematical Society Newsletter
Review
'Besides the usual topics ... there are some welcome geometrical illustrations, as well as some homespun philosophy.' Mathematica
Synopsis
In this book Miles Reid brings together algebra and geometry. He skilfully weaves together ideas from commutative ring theory and from algebraic geometry to form an attractive whole. The text is based on his lecture courses, given over several years to undergraduates and graduates at the University of Warwick. Here he has expanded those notes with customary wit, and many exercises and examples have been added. For those looking for an introduction to the area of commutative algebra, this book opens all the right doors and provides a clarity of understanding that all will welcome.
Synopsis
For those looking for an introduction to the area of commutative
Synopsis
Showing the link between commutative ring theory and algebraic geometry, this book contrasts the methods and ideology of modern abstract algebra with concrete applications in algebraic geometry and number theory. It is ideal for anyone seeking a primer on commutative algebra.
Description
Includes bibliographical references (p. 149) and index.
Table of Contents
Hello!; 1. Basics; 2. Modules; 3. Noetherian rings; 4. Finite extensions and Noether normalisation; 5. The nullstellensatz and spec A; 6. Rings of fractions S-1A and localisation; 7. Primary decomposition; 8. DVRs and normal integral domains; 9. Goodbye!; Bibliography.