Theorems · Theorem · commutative algebra

Valuation.IsEquiv.isTrivialOn_iff

∀ {R : Type u_3} {Γ₀ : Type u_4} {Γ'₀ : Type u_5} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀]
  [inst_2 : LinearOrderedCommMonoidWithZero Γ'₀] {v₁ : Valuation R Γ₀} {v₂ : Valuation R Γ'₀} {A : Type u_7}
  [inst_3 : CommSemiring A] [inst_4 : Algebra A R],
  v₁.IsEquiv v₂ → (Valuation.IsTrivialOn A v₁ ↔ Valuation.IsTrivialOn A v₂)

Defined in

Mathlib.RingTheory.Valuation.Basic

Cited by

0 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext

Assumes

RingLinearOrderedCommMonoidWithZeroLinearOrderedCommMonoidWithZeroCommSemiringAlgebra