Last updated: 19 Apr 2022.
*Georgia Tech no longer uses BlueJeans so the linked videos below are not available.
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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