Undergraduate Commutative Algebra

ISBN-13: 9780521458894 / Angielski / Miękka / 1995 / 168 str.

Miles Reid

Opis

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.

Recenzje

'Besides the usual topics … there are some welcome geometrical illustrations, as well as some homespun philosophy.' Mathematica

Spis treści

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.