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Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:category |
theorems in algebra
|
| gptkbp:field |
gptkb:algebra
gptkb:commutative_algebra |
| gptkbp:formedBy |
gptkb:David_Hilbert
|
| https://www.w3.org/2000/01/rdf-schema#label |
Hilbert's basis theorem
|
| gptkbp:implies |
Every ideal in a polynomial ring over a Noetherian ring is finitely generated.
|
| gptkbp:originalLanguage |
gptkb:German
|
| gptkbp:publicationYear |
1890
|
| gptkbp:publishedIn |
gptkb:Mathematische_Annalen
|
| gptkbp:relatedTo |
gptkb:Hilbert's_Nullstellensatz
Noetherian ring ideal theory |
| gptkbp:state |
If R is a Noetherian ring, then the polynomial ring R[x] is also Noetherian.
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
theory of ideals |
| gptkbp:bfsParent |
gptkb:David_Hilbert
|
| gptkbp:bfsLayer |
3
|