Cohen-Macaulay module
A module over a ring is a Cohen-Macaulay module if its depth is defined and equals its Krull dimension. A ring is said to be Cohen-Macaulay (or just C-M) if it is a Cohen-Macaulay module viewed as a module over itself.
Cohen-Macaulay rings are used extensively in combinatorial geometry and commutative ring theory, and has applications to algebraic geometry
as well. For instance, a variety all of whose local rings
are Cohen-Macaulay has, in a sense, nicer behaviour than an arbitrary singular variety.
| Title | Cohen-Macaulay module |
|---|---|
| Canonical name | CohenMacaulayModule |
| Date of creation | 2013-03-22 14:14:58 |
| Last modified on | 2013-03-22 14:14:58 |
| Owner | mathcam (2727) |
| Last modified by | mathcam (2727) |
| Numerical id | 6 |
| Author | mathcam (2727) |
| Entry type | Definition |
| Classification | msc 13C14 |
| Classification | msc 16E65 |
| Defines | Cohen-Macaulay ring |
| Defines | C-M module |
| Defines | C-M ring |