Theorems · Theorem · commutative algebra

IsDiscreteValuationRing.RingEquivClass.isDiscreteValuationRing

∀ {A : Type u_2} {B : Type u_3} {E : Type u_4} [inst : CommRing A] [inst_1 : IsDomain A] [inst_2 : CommRing B]
  [inst_3 : IsDomain B] [IsDiscreteValuationRing A] [inst_5 : EquivLike E A B] [RingEquivClass E A B] (e : E),
  IsDiscreteValuationRing B

If a ring is equivalent to a DVR, it is itself a DVR.

Defined in

Mathlib.RingTheory.DiscreteValuationRing.Basic

Cited by

0 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainCommRingIsDomainIsDiscreteValuationRingEquivLikeRingEquivClass