Theorems · Theorem · commutative algebra

NumberField.RingOfIntegers.withValEquiv_symm_apply

∀ {Γ₀ : Type u_2} [inst : LinearOrderedCommGroupWithZero Γ₀] {K : Type u_3} [inst_1 : Field K] (v : Valuation K Γ₀)
  (R : Type u_4) [inst_2 : CommRing R] [inst_3 : Algebra R K] [inst_4 : IsIntegralClosure R ℤ K] (a : R),
  (NumberField.RingOfIntegers.withValEquiv v R).symm a =
    (IsIntegralClosure.equiv ℤ R (WithVal v) (NumberField.RingOfIntegers (WithVal v))) a

Defined in

Mathlib.Topology.Algebra.Valued.WithVal

Cited by

0 results in Mathlib

Foundations

Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderedCommGroupWithZeroFieldCommRingAlgebraIsIntegralClosure