Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
finite field
|
| gptkbp:application |
used in the proof of Fermat's Last Theorem for regular primes
used in the study of cyclotomic fields |
| 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:algebra
gptkb:Galois_theory abstract algebra |
| https://www.w3.org/2000/01/rdf-schema#label |
Kummer extension
|
| gptkbp:introducedIn |
19th century
|
| gptkbp:namedAfter |
gptkb:Ernst_Kummer
|
| gptkbp:property |
Kummer extensions are abelian extensions.
Kummer extensions are cyclic if the base field contains a primitive n-th root of unity. |
| gptkbp:relatedTo |
gptkb:Artin–Schreier_extension
Galois extension cyclic extension |
| gptkbp:requires |
The base field must contain a primitive n-th root of unity.
|
| gptkbp:bfsParent |
gptkb:Algebraic_Number_Fields
gptkb:Kummer |
| gptkbp:bfsLayer |
7
|