**Math 205b: Commutative Algebra**

**Spring 2010**

What is new: Complete notes for course.

**Course information**

- Math 205b: Commutative Algebra
- Syllabus
- Text:
**Introduction to Commutative Algebra**by Atiyah and Macdonald. - Lecture format: Each class will consist of one hour of lecture and a half hour of discussion.
- Discussions: This means going over old and new exercises in class.
- Lecture notes: There will be detailed lecture notes posted online including details of proofs which I will skip in class.

- Instructor: Kiyoshi Igusa
- Location: Goldsmith 305
- Hours: TBA
- Phone 63062.
- email: igusa(at)brandeis(dot)edu

**Lecture Notes**

- Chap 1: Rings and ideals (combined file)
- Maximal ideals (identical to handout)
- Prime ideals (identical to handout)
- Algebraic Geometry (with one extra page of notes)

- Chap 2: Modules
- Modules and Nakayama (with one extra page of notes)
- Modules 2: tensor product

- Chap 3: Fractions in rings and modules
- Localization
- extension and contraction for localizations (same as handout.)

- Chap 4: Primary decomposition (completed)
- Chap 5: Integrality and valuations
- Chap 6: Chain conditions
- Chap 7: Noetherian rings
- Chap 8: Artinian rings
- Krull dimension is zero
- Characterization of Artinian rings
- Equivalent versions of Nakayama's Lemma (notes by Roger Lipsett)

- Chap 9: Discrete valuation rings
- Chap 10: Discrete valuation rings
- Chap 11: Dimension theory
- Complete notes

**Old Notes**

- Here are notes from a quick course on Commutative Algebra which was part of Math 101b, Spring 2007.

Home page: Kiyoshi Igusa | Office: | 305 Goldsmith | |||

Department of Mathematics | Phone: | (781) 736-3062 | Fax: (781) 736-3085 | Started: September 12, 2009 | |

Brandeis University | Email: | igusa@brandeis.edu | Last modified: May 14, 2010 |