Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
Used in the study of cyclotomic fields
Used in the proof of Fermat's Last Theorem for regular primes |
| gptkbp:characteristic |
Characteristic not dividing n
|
| gptkbp:defines |
A Kummer extension is a field extension obtained by adjoining an n-th root of an element to a field containing a primitive n-th root of unity.
|
| gptkbp:example |
The extension Q(√2)/Q is a Kummer extension.
|
| gptkbp:field |
gptkb:Algebraic_number_theory
|
| gptkbp:GaloisGroup |
Cyclic group of order dividing n
|
| https://www.w3.org/2000/01/rdf-schema#label |
Kummer extensions
|
| gptkbp:isA |
Field extension
Galois extension |
| gptkbp:namedAfter |
gptkb:Ernst_Eduard_Kummer
|
| gptkbp:relatedTo |
gptkb:Artin-Schreier_extensions
gptkb:Cyclotomic_extensions |
| gptkbp:requires |
Base field contains a primitive n-th root of unity
|
| gptkbp:bfsParent |
gptkb:Ernst_Eduard_Kummer
|
| gptkbp:bfsLayer |
5
|