Theorems · Theorem · commutative algebra
AddValuation.map_zero
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedAddCommMonoidWithTop Γ₀]
(v : AddValuation R Γ₀), v 0 = ⊤- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, 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.
- DFunLike.coestatement · cited by 62,936
- Top.topstatement · cited by 9,680
- Ringstatement and proof · cited by 7,463
- AddValuationstatement and proof · cited by 96
- LinearOrderedAddCommMonoidWithTopstatement and proof · cited by 68
- Valuation.map_zeroproof · cited by 11
Cited by5
Results whose statement or proof uses this declaration.
- Ring.ord_eq_addValproof · cited by 3
- IsDiscreteValuationRing.addVal_zeroproof · cited by 3
- IsDiscreteValuationRing.intValuation_maximalIdealproof · cited by 3
- IsDiscreteValuationRing.addVal_eq_zero_iffproof · cited by 0
- IsDiscreteValuationRing.addVal_eq_iff_associatedproof · cited by 0