Statements (13)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
Integral ring extensions
|
| gptkbp:describes |
Behavior of prime ideals under integral extensions
|
| gptkbp:field |
gptkb:Algebraic_geometry
gptkb:Commutative_algebra |
| https://www.w3.org/2000/01/rdf-schema#label |
Going-down theorem
|
| gptkbp:namedFor |
gptkb:Emil_Artin
|
| gptkbp:relatedTo |
gptkb:Going-up_theorem
|
| gptkbp:state |
If A ⊆ B is an integral extension and P ⊆ Q are prime ideals of A, and Q' is a prime ideal of B lying over Q, then there exists a prime ideal P' of B lying over P with P' ⊆ Q'
|
| gptkbp:usedIn |
Proofs in algebraic geometry
Proofs in commutative algebra |
| gptkbp:bfsParent |
gptkb:commutative_algebra
|
| gptkbp:bfsLayer |
5
|