Theorems · Theorem · commutative algebra
Valuation.map_mul
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] (v : Valuation R Γ₀)
(x y : R), v (x * y) = v x * v y- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 13 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.
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
- Ringstatement and proof · cited by 7,463
- Valuationstatement and proof · cited by 823
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- Valuation.toMonoidWithZeroHomproof · cited by 16
- MonoidWithZeroHom.map_mul'proof · cited by 2
Cited by13
Results whose statement or proof uses this declaration.
- Valuation.subgroups_basisproof · cited by 5
- AddValuation.map_mulproof · cited by 5
- Valuation.Integers.dvd_of_leproof · cited by 4
- Valuation.Integers.one_of_isUnit'proof · cited by 3
- Valuation.Integers.le_of_dvdproof · cited by 3
- IsDiscreteValuationRing.exists_lift_of_le_oneproof · cited by 2
- Valuation.Integers.isUnit_of_oneproof · cited by 2
- Valued.continuous_extensionproof · cited by 2
- ModP.mul_ne_zero_of_pow_p_ne_zeroproof · cited by 1
- Valuation.inversion_estimateproof · cited by 1
- ModP.preVal_mulproof · cited by 1
- PreTilt.isDomainproof · cited by 0