Proof readings and scope
The five lessons supply the decomposition, counting, field-extension and elimination arguments. Their exact earlier commutative-algebra readings are linked below with preserved source bodies and attribution.
Several-variable analysis
The module lesson proves its symbol-algebra theorem for finite-dimensional quotients of the complex polynomial ring on every connected open set. The full smooth-system fundamental principle on general convex open sets remains an unfinished analytic programme obligation; its density and integral-representation proof is not supplied in this bundle.
Earlier commutative algebra
- Spectra of rings
- Spectral spaces and affine realization
- Localization, local properties and support
- Noetherian and Artinian rings
- Associated primes and primary decomposition
- Integral extensions: lying over, going up and going down
- The Nullstellensatz and Jacobson rings
- Resolutions, Tor and Ext
- Tor and flat modules
- Krull dimension and Noether normalization
- Graded modules and Hilbert–Samuel functions
- Dimension theory of Noetherian local rings
- Regular sequences, depth and Cohen–Macaulay modules
- Projective dimension and the Auslander–Buchsbaum formula
- Regular local rings
- Kähler differentials