Theorems · Definition · commutative algebra
Rat.ringOfIntegersWithValEquiv
{Γ₀ : Type u_2} →
[inst : LinearOrderedCommGroupWithZero Γ₀] → (v : Valuation ℚ Γ₀) → NumberField.RingOfIntegers (WithVal v) ≃+* ℤThe ring of integers of WithVal v, when v is a valuation on ℚ, is
equivalent to ℤ.
- Defined in
- Mathlib.Topology.Algebra.Valued.WithVal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 152 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.
- RingEquivstatement · cited by 1,147
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- NumberField.RingOfIntegersstatement · cited by 413
- WithValstatement · cited by 151
- NumberField.RingOfIntegers.withValEquivproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Rat.ringOfIntegersWithValEquiv_applystatement and proof · cited by 0