Theorems · Theorem · field theory

Irreducible.maximalIdeal_eq_closedBall

∀ {K : Type u_1} [inst : NontriviallyNormedField K] [inst_1 : IsUltrametricDist K]
  [IsDiscreteValuationRing ↥(Valued.integer K)] {ϖ : ↥(Valued.integer K)},
  Irreducible ϖ → ↑(Valued.maximalIdeal K) = Metric.closedBall 0 ‖ϖ‖

Defined in: Mathlib.Topology.Algebra.Valued.LocallyCompact
Cited by: 0 results in Mathlib
Foundations: Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NontriviallyNormedField IsUltrametricDist IsDiscreteValuationRing

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites19

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
NontriviallyNormedFieldstatement and proof · cited by 8,742
SetLike.coestatement · cited by 8,199
Set.ofPredproof · cited by 6,101
Norm.normstatement and proof · cited by 5,413
Idealstatement · cited by 4,748
NNRealstatement · cited by 4,310
Metric.closedBallstatement and proof · cited by 704
Subringstatement · cited by 602
Irreduciblestatement and proof · cited by 496
IsUltrametricDiststatement and proof · cited by 177
dist_zero_rightproof · cited by 172

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.