Theorems · Definition · field theory
Valued.integer
(K : Type u_1) →
[inst : Field K] →
{Γ₀ : outParam (Type u_2)} → [inst_1 : LinearOrderedCommGroupWithZero Γ₀] → [vK : Valued K Γ₀] → Subring KA Valued version of Valuation.integer, enabling the notation 𝒪[K] for the
valuation integers of a valued field K.
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Subringstatement · cited by 602
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Valued.vproof · cited by 163
- Valuedstatement and proof · cited by 70
- Valuation.integerproof · cited by 68
Cited by27
Results whose statement or proof uses this declaration.
- Valued.ResidueFieldproof · cited by 4
- Rat.HeightOneSpectrum.adicCompletionIntegers.padicIntEquivproof · cited by 4
- Valued.maximalIdealstatement and proof · cited by 4
- Valued.integer.exists_norm_coe_lt_onestatement · cited by 2
- Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integerstatement and proof · cited by 2
- Valued.integer.finite_quotient_maximalIdeal_pow_of_finite_residueFieldstatement and proof · cited by 1
- Valued.integer.isDiscreteValuationRing_of_compactSpacestatement and proof · cited by 1
- Valued.integer.isPrincipalIdealRing_of_compactSpacestatement and proof · cited by 1
- Valued.integer.mem_iffstatement · cited by 1
- Valued.integer.mulArchimedean_mrange_of_isCompact_integerstatement and proof · cited by 1
- Valued.integer.norm_coe_unitstatement and proof · cited by 1
- Valued.integer.totallyBounded_iff_finite_residueFieldstatement and proof · cited by 1