2023–24–A

Prof. Amnon Yekutieli

Abstract

Teaching method: ZOOM lectures.

Active web page: https://sites.google.com/view/amyekut-math/home/teaching/comm-alg-2023-24-a

Prerequisite: Introduction to Commutative Algebra

Ignore file “syllabus ver 1” and the entry in the BGU course catalog. See file “Syllabus ver 2”

Topics: 1. Recalling basic commutative algebra. 2. More basic commutative algebra. 3. Limits in algebra. 4. Adic completion. 5. Completion of noetherian rings. 6. Complete local rings. 7. Differential commutative algebra. 8. Étale ring homomorphisms. 9. 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.

University course catalogue: 201.2.2011