13B40 Étale and flat extensions; Henselization; Artin approximation [See also <a href="#code:13J15">13J15</a>, <a href="#code:14B12">14B12</a>, <a href="#code:14B25">14B25</a>]

13B99 None of the above, but in this section

13C10 Projective and free modules and ideals [See also <a href="#code:19A13">19A13</a>]

13C11 Injective and flat modules and ideals

13C14 Cohen-Macaulay modules [See also <a href="#code:13H10">13H10</a>]

13C15 Dimension theory, depth, related rings (catenary, etc.)

13C20 Class groups [See also <a href="#code:11R29">11R29</a>]

13C40 Linkage, complete intersections and determinantal ideals [See also <a href="#code:14M06">14M06</a>, <a href="#code:14M10">14M10</a>, <a href="#code:14M12">14M12</a>]

13C99 None of the above, but in this section

13Dxx Homological methods {For noncommutative rings, see <a href="#code:16Exx">16Exx</a>; for general categories, see <a href="#code:18Gxx">18Gxx</a>}

13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)

13D07 Homological functors on modules (Tor, Ext, etc.)

13D10 Deformations and infinitesimal methods [See also <a href="#code:14B10">14B10</a>, <a href="#code:14B12">14B12</a>, <a href="#code:14D15">14D15</a>, <a href="#code:32Gxx">32Gxx</a>]

13D15 Grothendieck groups, $K$-theory [See also <a href="#code:14C35">14C35</a>, <a href="#code:18F30">18F30</a>, <a href="#code:19Axx">19Axx</a>, <a href="#code:19D50">19D50</a>]

13D22 Homological conjectures (intersection theorems)

13D30 Torsion theory [See also <a href="#code:13C12">13C12</a>, <a href="#code:18E40">18E40</a>]

13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series

13D45 Local cohomology [See also <a href="#code:14B15">14B15</a>]

13D99 None of the above, but in this section

13Exx Chain conditions, finiteness conditions

13E10 Artinian rings and modules, finite-dimensional algebras

13E15 Rings and modules of finite generation or presentation; number of generators

13E99 None of the above, but in this section

13Fxx Arithmetic rings and other special rings