Prof. Amnon Yekutieli


Topics: 1. Recalling basic commutative algebra. 2. Limits in algebra. 3. Adic completion. 4. Completion of noetherian rings. 5. Complete local rings. 6. Differential commutative algebra. 7. Étale ring homomorphisms. 8. Smooth ring homomorphisms.

Course topics

Course Topics
  1. Modules: free modules, exact sequences, tensor products, Hom modules, flatness.
  2. Prime ideals and localization: local rings, Nakayama’s Lemma, the spectrum of a ring, dimension and connectedness.
  3. Noetherian rings: the Hilbert basis theorem, the Artin-Rees lemma, completion, grading.
  4. Dimension theory: the Hilbert nullstellensatz, Noether normalization, transcendence degree.

Requirements and grading

Prerequisite: Introduction to Commutative Algebra

Grading: pass/fail

Teaching method: ZOOM lectures.

Active web page: https://sites.google.com/view/amyekut-math/home

Ignore old syllabus “course topics”

University course catalogue: 201.2.2011