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Homological methods

{For commutative rings, see 13Dxx; for general categories, see 18Gxx }
16E05 Syzygies, resolutions, complexes
16E10 Homological dimension
16E20 Grothendieck groups, $K$-theory, etc. [See also 18F30, 19Axx, 19D50]
16E30 Homological functors on modules (Tor, Ext, etc.)
16E40 (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
16E45 Differential graded algebras and applications
16E50 von Neumann regular rings and generalizations
16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.
16E65 Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
16E99 None of the above, but in this section