Spring 2022: Math 6122 (Algebra II: Intro to commutative algebra)

This spring I am teaching Math 6122, Algebra II: Intro to commutative algebra.

My office hours are Tuesdays, Wednesdays, and Thursdays from 530-630p. For everyone’s safety my office hours are virtual. Use the BlueJeans link in the syllabus.

This course uses Mel Hochster’s lecture notes and exercises. Other references can be found in the syllabus.

See Canvas for announcements related to the course. The recorded lectures are posted here (you must be a member of the Georgia Tech organization to view them):

Tues 11 Jan: Questions and categories

Thurs 13 Jan: Spec and natural transformations (fast forward to 3:25)

Tues 18 Jan: Representable functors and semigroup algebras (fast forward to 2:45)

Thurs 20 Jan: Semigroup algebras and multiplicative systems (fast forward to 17:38 to skip the quiz)

Tues 25 Jan: Localizations

Thurs 27 Jan: Spec(R) and integral extensions

Tues 1 Feb: Integral extensions

Thurs 3 Feb: Integral extensions and integral closure

Tues 8 Feb (no recording available): Going down theorem

Thurs 10 Feb: Noether normalization and Hilbert’s Nullstellensatz

Tues 15 Feb: Transcendence degree and DVRs

Thurs 17 Feb: Chain conditions on modules

Tues 22 Feb: Annihilators and Hilbert’s basis theorem

Thurs 24 Feb: Noetherian induction and Hilbert’s Nullstellensatz again

Tues 1 Mar: Antiequivalence of categories of algebraic sets and reduced finitely generated K-algebras

Thurs 3 Mar: Formal power series rings

Tues 8 Mar: Tensor products

Thurs 10 Mar: Tensor products

Tues 15 Mar: Tensor and Hom

Thurs 17 Mar: Flat R-modules

Tues 29 Mar: Local properties

Thurs 31 Mar: Adjointness of tensor and Hom

Thurs 7 Apr: Nakayama’s lemma

Tues 12 Apr: Primary decomposition

Thurs 14 Apr: Primary decomposition

Tues 19 Apr: Primary decomposition