Theorems · Definition · commutative algebra
WithVal.valueGroupEquiv
{Γ₀ : Type u_2} →
[inst : LinearOrderedCommGroupWithZero Γ₀] →
{R : Type u_3} →
[inst_1 : Ring R] →
(v : Valuation R Γ₀) →
↥(MonoidWithZeroHom.ofClass Valued.v).valueGroup ≃* ↥(MonoidWithZeroHom.ofClass v).valueGroupThe multiplicative equivalence between the valueGroup of the valuation on WithVal v
and the valuation v.
- Defined in
- Mathlib.Topology.Algebra.Valued.WithVal
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- SetLike.coeproof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Set.Elemproof · cited by 7,166
- Subgroupstatement · cited by 3,593
- Unitsstatement · cited by 2,804
- MulEquivstatement · cited by 1,142
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MonoidWithZeroHom.ofClassstatement and proof · cited by 204
- MonoidWithZeroHom.valueGroupstatement and proof · cited by 170
- Valued.vstatement and proof · cited by 163
Cited by9
Results whose statement or proof uses this declaration.
- WithVal.valueGroupOrderIso₀proof · cited by 7
- WithVal.valueGroupEquiv_applystatement and proof · cited by 2
- WithVal.valueGroupEquiv_symm_applystatement and proof · cited by 2
- WithVal.strictMono_valueGroupEquiv_symmstatement · cited by 1
- WithVal.valueGroupOrderIso₀_applystatement · cited by 1
- WithVal.strictMono_valueGroupEquivstatement · cited by 1
- WithVal.valueGroupOrderIso₀_symm_applystatement · cited by 1
- WithVal.valueGroupOrderIso₀_restrictproof · cited by 1
- WithVal.valueGroupOrderIso₀_symm_restrictproof · cited by 0