Theorems · Theorem · commutative algebra
Valuation.map_zero
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] (v : Valuation R Γ₀),
v 0 = 0- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Valuationstatement and proof · cited by 823
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- MonoidWithZeroHom.toZeroHomproof · cited by 35
- Valuation.toMonoidWithZeroHomproof · cited by 16
- ZeroHom.map_zero'proof · cited by 7
Cited by11
Results whose statement or proof uses this declaration.
- Valuation.IsEquiv.eq_zeroproof · cited by 11
- AddValuation.map_zeroproof · cited by 5
- IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvdproof · cited by 5
- Valuation.Integers.dvd_of_leproof · cited by 4
- Valuation.map_sum_ltproof · cited by 4
- ValuationSubring.valuation_eq_one_iffproof · cited by 2
- Valuation.map_sum_leproof · cited by 2
- PowerSeries.intValuation_eq_of_coeproof · cited by 2
- PreTilt.map_eq_zeroproof · cited by 1
- Valuation.inversion_estimateproof · cited by 1
- Valued.closure_coe_completion_v_ltproof · cited by 1