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Mathematical Sciences Classification System

13Dxx - Homological methods
{For noncommutative rings, see 16Exx; for general categories, see 18Gxx}

• 10
  13D02
  Syzygies, resolutions, complexes
• 2
  13D03
  (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
• 2
  13D05
  Homological dimension
• 13D07
  Homological functors on modules (Tor, Ext, etc.)
• 1
  13D09
  Derived categories
• 3
  13D10
  Deformations and infinitesimal methods [See also 14B10, 14B12, 14D15, 32Gxx]
• 1
  13D15
  Grothendieck groups, $K$-theory [See also 14C35, 18F30, 19Axx, 19D50]
• 13D22
  Homological conjectures (intersection theorems)
• 13D25
  Complexes
• 1
  13D30
  Torsion theory [See also 13C12, 18E40]
• 4
  13D40
  Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
• 6
  13D45
  Local cohomology [See also 14B15]
• 13D99
  None of the above, but in this section