Theorems · Theorem · commutative algebra

Valuation.Integers.le_iff_dvd

∀ {F : Type u} {Γ₀ : Type v} [inst : Field F] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] {v : Valuation F Γ₀}
  {O : Type w} [inst_2 : CommRing O] [inst_3 : Algebra O F],
  v.Integers O → ∀ {x y : O}, v ((algebraMap O F) x) ≤ v ((algebraMap O F) y) ↔ y ∣ x

Defined in

Mathlib.RingTheory.Valuation.Integers

Cited by

5 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderedCommGroupWithZeroCommRingAlgebra