Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:citation |
gptkb:Eisenbud,_D.,_Commutative_Algebra_with_a_View_Toward_Algebraic_Geometry
Atiyah, M. F.; Macdonald, I. G., Introduction to Commutative Algebra |
| gptkbp:defines |
An extension of rings R ⊆ S such that every element of S is integral over R
|
| gptkbp:example |
The ring of complex numbers is an integral extension of the real numbers
The ring of algebraic integers is an integral extension of the integers |
| gptkbp:field |
gptkb:algebra
gptkb:Commutative_algebra |
| https://www.w3.org/2000/01/rdf-schema#label |
Integral extensions
|
| gptkbp:property |
If S is an integral extension of R, then S is a module-finite R-algebra
If S is an integral extension of R, then the going-up theorem holds If S is an integral extension of R, then the spectrum map Spec(S) → Spec(R) is surjective |
| gptkbp:relatedConcept |
Noetherian ring
Algebraic extension Integral element Module-finite extension |
| gptkbp:relatedTo |
gptkb:Ring_theory
|
| gptkbp:bfsParent |
gptkb:Going-up_theorem
|
| gptkbp:bfsLayer |
6
|