# Math 380a/500a

Introductory commutative algebra from David Eisenbud's book Commutative Algebra with a View Toward Algebraic Geometry.

## Office hours

• Office hours: F 2-4
• Office: 219B LOM

## Announcements

• Dec. 3: Office hours 2-4pm.
• Nov. 22: Office hours semi-cancelled. If I'm around, you can stop by, but no guarantees.
• Sep. 19: No class on Sep. 30 or Oct. 21. Make-up classes on Friday, Sep. 27 and Friday, Oct. 18 at 9:45-11:00am in 431 DL.
• Sep. 17: Starting this week, Wednesday office hours will be replaced by extended office hours on Friday.

## Final exam

Here are solutions to the final exam.

## Homeworks

Homework is due most Mondays and the assignments will be posted here. Solutions or partial solutions to some of these assignments are available on request.

## Schedule

The approximate schedule for future classes is given in the following table. All readings are from Eisenbud.

 Date Reading Topics Aug. 28 Ch. 0 (and 1) origins of commutative algebra Aug. 30 2.1 localization and Hom Sep. 4 2.2 tensor products and flatness of localization Sep. 9 2.3, 2.4 radical, modules of finite length Sep. 11 3.1, 3.2 prime avoidence, associated primes Sep. 16 3.3 primary decomposition Sep. 18 none localization of primary decomposition, Nullstellensatz Sep. 23 4.1 integrality and Nakayama's lemma Sep. 25 4.2,4.4 primes in integral extensions Sep. 27 4.5 proof of Nullstellensatz Oct. 2 5.1 finish Nullstellensatz, associated graded Oct. 7 5.2, 5.3, 6.1 (optional), 6.2 Artin-Reese Lemma, Krull Intersection Theorem, flatness, Tor Oct. 9 6.3 (through Cor. 6.3), 6.5 criterion for flatness, Rees algebra Oct. 14 7.1, 7.2, 7.5 completions Oct. 16 7.6 flatness of completion, maps from power series Oct. 18 9.0, 10.0 statement of Cohen structure theorem, Krull dimension, PIT Oct. 28 10.1, 10.2 systems of parameters, going down theorem Oct. 30 10.3, 11.1 regular local ring, DVRs Nov. 4 11.2 Serre's criterion, class group Nov 6 11.6 Krull-Akizuki theorem Nov. 11 12 Hilbert-Samuel polynomial Nov. 13 13.1 Noether normalization Nov. 18 13.1 Consequences of Noether normalization Nov. 20 13.3 finiteness of integral closure Dec. 2 15.1, 15.2, 15.3 monomials and division Dec. 4 15.4, 15.8 Gröbner bases