Commutative algebra is the theoretical foundation of algebraic geometry and algebraic number theory. Assuming as prerequisite a standard graduate algebra course, we attempt to reach an advanced level quickly and efficiently.

## Book Description

The idea is to help the student reach an advanced level as quickly and efficiently as possible. In Chapter 1, the theory of primary decomposition is developed so as to apply to modules as well as ideals.

## Table of Contents

- Ring Theory Background
- Primary Decomposition and Associated Primes
- Integral Extensions
- Valuation Rings
- Completion
- Dimension Theory
- Depth
- Homological Methods
- Regular Local Rings