Math 380a/500a

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

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Final exam

Here are solutions to the final exam.


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.


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

Aug. 28Ch. 0 (and 1)origins of commutative algebra
Aug. 302.1localization and Hom
Sep. 42.2tensor products and flatness of localization
Sep. 92.3, 2.4 radical, modules of finite length
Sep. 113.1, 3.2 prime avoidence, associated primes
Sep. 163.3primary decomposition
Sep. 18nonelocalization of primary decomposition, Nullstellensatz
Sep. 234.1integrality and Nakayama's lemma
Sep. 254.2,4.4primes in integral extensions
Sep. 274.5proof of Nullstellensatz
Oct. 25.1finish Nullstellensatz, associated graded
Oct. 75.2, 5.3, 6.1 (optional), 6.2Artin-Reese Lemma, Krull Intersection Theorem, flatness, Tor
Oct. 96.3 (through Cor. 6.3), 6.5criterion for flatness, Rees algebra
Oct. 147.1, 7.2, 7.5completions
Oct. 167.6 flatness of completion, maps from power series
Oct. 189.0, 10.0 statement of Cohen structure theorem, Krull dimension, PIT
Oct. 2810.1, 10.2 systems of parameters, going down theorem
Oct. 3010.3, 11.1 regular local ring, DVRs
Nov. 411.2 Serre's criterion, class group
Nov 611.6 Krull-Akizuki theorem
Nov. 1112Hilbert-Samuel polynomial
Nov. 1313.1Noether normalization
Nov. 1813.1Consequences of Noether normalization
Nov. 2013.3finiteness of integral closure
Dec. 215.1, 15.2, 15.3monomials and division
Dec. 415.4, 15.8Gröbner bases