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Theorems · Definition · field theory

Valued.ResidueField

(K : Type u_1) →
  [inst : Field K] →
    {Γ₀ : outParam (Type u_2)} → [inst_1 : LinearOrderedCommGroupWithZero Γ₀] → [vK : Valued K Γ₀] → Type u_1

An abbreviation for IsLocalRing.ResidueField 𝒪[K] of a Valued instance, enabling the notation 𝓀[K] for the residue field of a valued field K.

Defined in
Mathlib.Topology.Algebra.Valued.ValuedField
Cited by
4 results in Mathlib
Foundations
Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldLinearOrderedCommGroupWithZeroValued
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Valued.integer.finite_quotient_maximalIdeal_pow_of_finite_residueField · cited by 1integer.finite_quotient_m…Valued.integer.totallyBounded_iff_finite_residueField · cited by 1integer.totallyBounded_if…Valued.integer.properSpace_iff_completeSpace_and_isDiscreteValuationRing_integer_and_finite_residueField · cited by 0integer.properSpace_iff_c…Valued.integer.compactSpace_iff_completeSpace_and_isDiscreteValuationRing_and_finite_residueField · cited by 0integer.compactSpace_iff_…Field · cited by 7404FieldLinearOrderedCommGroupWithZero · cited by 528LinearOrderedCommGroupWit…IsLocalRing.ResidueField · cited by 156IsLocalRing.ResidueFieldValued · cited by 70ValuedValued.integer · cited by 22Valued.integerValued.ResidueFieldCITED BYCITES

Cites5

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

Cited by4

Results whose statement or proof uses this declaration.