Statements (16)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:concerns |
finitely generated module
projective dimension Noetherian local ring |
| gptkbp:field |
gptkb:commutative_algebra
|
| https://www.w3.org/2000/01/rdf-schema#label |
Auslander–Buchsbaum theorem
|
| gptkbp:namedAfter |
gptkb:David_Buchsbaum
gptkb:Maurice_Auslander |
| gptkbp:publicationYear |
1957
|
| gptkbp:publishedIn |
gptkb:Proceedings_of_the_National_Academy_of_Sciences
|
| gptkbp:relatedTo |
gptkb:syzygy_theorem
homological algebra depth (ring theory) |
| gptkbp:state |
If M is a nonzero finitely generated module over a Noetherian local ring R, and M has finite projective dimension, then the projective dimension of M plus the depth of M equals the depth of R.
|
| gptkbp:bfsParent |
gptkb:David_Buchsbaum
|
| gptkbp:bfsLayer |
6
|