## Math 470-3: Graduate Algebra, Spring 2010

**MWF 12pm, Lunt 102**

**Instructor:** Florian Herzig

**Office:** Lunt 309

**Phone:** 467-1898

**E-mail:** my last name at math dot northwestern dot edu

**Office Hours:** Wed 5:00-6:30, Fri 1:30-3:00

**Note:** This page will be updated as the course progresses.
### Course description

This is the third quarter of the graduate algebra sequence. This term the main focus is on commutative algebra.
### Topics to be covered

- Local rings, Nakayama's lemma, localisation
- Noetherian and artinian rings, Nullstellensatz, Spec
- Integral extensions, going up
- Support and associated primes
- Artin-Rees lemma, completions
- Dimension theory
- DVRs and Dedekind domains

### Prerequisites

I will assume that you have taken a standard honors algebra course on groups, rings, and fields, as well as some basic topology.
### Textbook

- Serge Lang:
*Algebra*, revised 3rd ed., Springer or Addison-Wesley

We will not follow Lang very closely, but stay closer to Atiyah-Macdonald.
Other general books on algebra:
- Nathan Jacobson:
*Basic Algebra* (2 volumes)

Commutative algebra:
- Michael Atiyah, Ian Macdonald:
*Introduction to Commutative Algebra* (Westview Press); the classic introductory textbook
- Miles Reid:
*Undergraduate Commutative Algebra* (LMS Student Texts); an excellent introduction that brings out the connections to algebraic geometry;
covers less than the other books
- Hideyuki Matsumura:
*Commutative Ring Theory* (Cambridge); contains a lot more than what we will cover
- James Milne's course notes

### Homework

Problem Set 1

Problem Set 2

Problem Set 3
### Links

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