| 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 |