Theorems · Theorem · commutative algebra

Valuation.Integers.dvdNotUnit_iff_lt

∀ {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}, DvdNotUnit x y ↔ v ((algebraMap O F) y) < v ((algebraMap O F) x)

Defined in

Mathlib.RingTheory.Valuation.Integers

Cited by

1 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderedCommGroupWithZeroCommRingAlgebra