Theorems · Theorem · commutative algebra

Valuation.Integers.exists_of_le_one

∀ {R : Type u} {Γ₀ : Type v} [inst : CommRing R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] {v : Valuation R Γ₀}
  {O : Type w} [inst_2 : CommRing O] [inst_3 : Algebra O R],
  v.Integers O → ∀ ⦃r : R⦄, v r ≤ 1 → ∃ x, (algebraMap O R) x = r

Defined in

Mathlib.RingTheory.Valuation.Integers

Cited by

9 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLinearOrderedCommGroupWithZeroCommRingAlgebra