Theorems · Theorem · commutative algebra

Ring.ord_eq_addVal

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDiscreteValuationRing R] (x : R),
  Ring.ord R x = (IsDiscreteValuationRing.addVal R) x

In a discrete valuation ring, ord R x is the same as addVal R x. We prefer the second spelling here for most purposes.

Defined in

Mathlib.RingTheory.OrderOfVanishing.Noetherian

Cited by

3 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainIsDiscreteValuationRing