Lecture Times: TR 11 AM - 12:20 PM
Class Location: Phil Smith Hall (BU) 112
Commutative Algebra, the study of commutative rings, is a bit of an unsung hero in modern mathematics. It has been a major engine of progress in algebraic geometry, where coordinate rings describe algebraic varieties, and number theory, where many results emerge from studying extensions of the ring of integers.
This course will introduce you to the basic players of commutative algebra: rings, ideals, modules, and sequences. We will also prove and apply some important basic results including Nakayama’s Lemma, the Nullstellensatz, and the Hilbert Basis Theorem.
From the FAU Catalog: An introduction to commutative rings. Topics include ideals, modules, rings and modules of fractions, integral dependence and valuations and chain conditions (Noetherian and Artinian rings).
Most class business -- including homework and quizzes -- will be managed on the Canvas site.
UPDATE 12/10/25: Since posting this course on YouTube, I have received several requests to post the notes from the lecture videos. I am including them below:
| # | Title | Video | Notes |
|---|---|---|---|
| 0 | Introduction | YouTube | Notes |
| 1 | Rings | YouTube | Notes |
| 2 | Ideals | YouTube | Notes |
| 3 | Operations on Ideals | YouTube | Notes |
| 4 | Two Ideal Theorems | YouTube | Notes |
| 5 | Spec | YouTube | Notes |
| 6 | Modules | YouTube | Notes |
| 7 | Two Module Theorems | YouTube | Notes |
| 8 | Exact Sequences & Hom | YouTube | Notes |
| 9 | Tensor Product | YouTube | Notes |
| 10 | Flat Modules | YouTube | Notes |
| 11 | Localization — Definition & Examples | YouTube | Notes |
| 12 | Localization — Functorial Perspective | YouTube | Notes |
| 13 | Primary Decomposition | YouTube | Notes |
| 14 | Integral Extensions | YouTube | Notes |
| 15 | Cohen–Seidenberg Theorems | YouTube | Notes |
| 16 | Valuation Rings | YouTube | Notes |
| 17 | Nullstellensatz |
YouTube (Part 1) YouTube (Part 2) |
Notes |
| 18 | Chain Conditions | YouTube | Notes |
| 19 | Noetherian Rings | YouTube | Notes |
| 20 | Artin Rings | YouTube | Notes |
| 21 | Graded Rings & Modules | YouTube | Notes |