Ideal theory in rings

Noether’s intersection theory: irreducible and primary components, isolated sets, relative and coprime decompositions, module examples, generic zeros, absolute primality, and resultant forms.

• Chain conditions and irreducible decompositions
  Lesson 1 of 5
• Primary ideals and isolated components
  Lesson 2 of 5
• Modules, staircases and elementary divisors
  Lesson 3 of 5
• Generic zeros and absolute primality
  Lesson 4 of 5
• Resultant forms and elimination
  Lesson 5 of 5

Historical readings

• Ideal Theory in Ring Domains
• On the Theory of Polynomial Ideals and Resultants
• Elimination Theory and General Ideal Theory

Prerequisite readings

The linked source snapshots carry their attribution and component notices.

• 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

Editable sources

Complete LaTeX source · Complete source archive