Math 470-3: Graduate Algebra, Spring 2010
MWF 12pm, Lunt 102
Instructor: Florian Herzig
Office: Lunt 309
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.
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
I will assume that you have taken a standard honors algebra course on groups, rings, and fields, as well as some basic topology.
We will not follow Lang very closely, but stay closer to Atiyah-Macdonald.
Other general books on algebra:
- Serge Lang: Algebra, revised 3rd ed., Springer or Addison-Wesley
- Nathan Jacobson: Basic Algebra (2 volumes)
- 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
Problem Set 1
Problem Set 2
Problem Set 3
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