Theorems · Theorem · commutative algebra
Valuation.map_pow
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] (v : Valuation R Γ₀)
(x : R) (n : ℕ), v (x ^ n) = v x ^ n- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 4 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.toMonoidHomproof · cited by 39
- MonoidHom.map_powproof · cited by 30
- Valuation.toMonoidWithZeroHomproof · cited by 16
Cited by4
Results whose statement or proof uses this declaration.
- AddValuation.map_powproof · cited by 5
- PreTilt.valAux_eqproof · cited by 4
- ModP.mul_ne_zero_of_pow_p_ne_zeroproof · cited by 1
- AlgebraicGeometry.Proj.valuativeCriterion_existence_auxproof · cited by 1