Bourbaki

Book AC · English

Commutative Algebra

Algèbre commutative

Start reading → Flat modules

  1. Front matter
    1. Introduction
    2. To the reader
  2. IFlat modules
    1. Flat modules
    2. § 1. Diagrams and exact sequences7
    3. § 2. Flat modules37
    4. § 3. Faithfully flat modules18
    5. § 4. Flat modules and "Tor" functors3
  3. IILocalization
    1. Localization
    2. § 1. Prime ideals9
    3. § 2. Rings and modules of fractions52
    4. § 3. Local rings. Passage from the local to the global39
    5. § 4. Spectra of rings and supports of modules49
    6. § 5. Finitely generated projective modules. Invertible fractional ideals34
  4. IIIGraduations. Filtrations and topologies
    1. Graduations. Filtrations and topologies
    2. § 1. Finitely generated graded algebras13
    3. § 2. General results on filtered rings and modules57
    4. § 3. m-adic topologies on Noetherian rings39
    5. § 4. Lifting in complete rings23
    6. § 5. Flatness properties of filtered modules11
  5. IVAssociated prime ideals and primary decomposition
    1. Associated prime ideals and primary decomposition
    2. § 1. Prime ideals associated with a module24
    3. § 2. Primary decomposition39
    4. § 3. Primary decomposition in graded modules6
  6. VIntegers
    1. Integers
    2. § 1. Notion of an integral element69
    3. § 2. The lift of prime ideals36
    4. § 3. Finitely generated algebras over a field17
  7. VIValuations
    1. Valuations
    2. § 1. Valuation rings15
    3. § 2. Places9
    4. § 3. Valuations15
    5. § 4. The height of a valuation18
    6. § 5. The topology defined by a valuation10
    7. § 6. Absolute values11
    8. § 7. Approximation theorem14
    9. § 8. Extensions of a valuation to an algebraic extension36
    10. § 9. Application: locally compact fields10
    11. § 10. Extensions of a valuation to a transcendental extension14
  8. VIIDivisors
    1. Divisors
    2. § 1. Krull domains41
    3. § 2. Dedekind domains15
    4. § 3. Factorial domains19
    5. § 4. Modules over integrally closed Noetherian domains56
    6. Historical Note
  9. Indexes
    1. Index of notation
    2. Index of terminology