Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
cyclic Galois extensions
|
| gptkbp:cohomologicalInterpretation |
H^1(Gal(K/F), K^×) = 0
|
| gptkbp:field |
gptkb:algebra
gptkb:Galois_cohomology |
| gptkbp:generalizes |
gptkb:Kummer_theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Hilbert's Theorem 90
|
| gptkbp:namedAfter |
gptkb:David_Hilbert
|
| gptkbp:publishedIn |
gptkb:Zahlbericht
|
| gptkbp:relatedTo |
gptkb:Galois_theory
cohomology |
| gptkbp:sentence |
If K/F is a cyclic Galois extension with Galois group generated by σ, then every element of norm 1 in K can be written as x/σ(x) for some x in K.
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
algebraic number theory class field theory |
| gptkbp:year |
1897
|
| gptkbp:bfsParent |
gptkb:Kummer_theory
gptkb:Galois_cohomology |
| gptkbp:bfsLayer |
6
|