Theoretical / proof-based
Commutative algebra · Graduate · Math
Topics
Rings and modules
- Noetherian and Artinian rings and modules
- Primary decomposition in Noetherian rings
- Integral extensions and going-up/going-down theorems
- Dedekind domains and DVRs
- Tensor products and flatness (introduction)
Localization and dimension
- Localization of rings and modules
- Spec(R) and Zariski topology (commutative algebra view)
- Krull dimension and height of primes
- Hilbert's Nullstellensatz and connections to geometry
- Regular sequences and Cohen–Macaulay rings (introduction)
Homological algebra tools
- Projective and injective modules; resolutions
- Ext and Tor functors (definitions and basic computations)
- Depth and Auslander–Buchsbaum formula (introduction)
- Completion and Hensel's lemma
- Smooth and étale morphisms (preview)
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$1,162 · Commutative algebra · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle or Venmo.