Theorems · Theorem · field theory
IsUltrametricDist.algNormOfAlgEquiv_extends
∀ {K : Type u_1} [inst : NormedField K] {L : Type u_2} [inst_1 : Field L] [inst_2 : Algebra K L]
[h_fin : FiniteDimensional K L] [hu : IsUltrametricDist K] (σ : Gal(L/K)) (x : K),
(IsUltrametricDist.algNormOfAlgEquiv σ) ((algebraMap K L) x) = ‖x‖The algebra norm algNormOfAlgEquiv extends the norm on K.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Norm.normstatement and proof · cited by 5,413
- Algebra.algebraMapstatement · cited by 4,706
- FiniteDimensionalstatement and proof · cited by 1,854
- AlgEquivstatement and proof · cited by 1,681
- NormedFieldstatement and proof · cited by 1,084
- IsUltrametricDiststatement and proof · cited by 177
- AlgEquiv.commutesproof · cited by 49
Cited by1
Results whose statement or proof uses this declaration.
- IsUltrametricDist.invariantExtension_extendsproof · cited by 1