Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
gptkb:algebraic_geometry
homological algebra singularity theory |
| gptkbp:citation |
gptkb:Matsumura,_Commutative_Ring_Theory
Bruns and Herzog, Cohen–Macaulay Rings |
| gptkbp:defines |
A Noetherian ring in which the depth equals the Krull dimension
|
| gptkbp:field |
gptkb:commutative_algebra
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cohen–Macaulay rings
|
| gptkbp:introducedIn |
1946
|
| gptkbp:namedAfter |
gptkb:Francis_S._Macaulay
gptkb:Irving_S._Cohen |
| gptkbp:property |
all regular local rings are Cohen–Macaulay
generalization of regular rings not all Cohen–Macaulay rings are regular all complete intersection rings are Cohen–Macaulay |
| gptkbp:relatedConcept |
gptkb:Gorenstein_ring
gptkb:Krull_dimension gptkb:regular_ring Noetherian ring depth |
| gptkbp:bfsParent |
gptkb:Gorenstein_rings
|
| gptkbp:bfsLayer |
7
|