Mathlib Map

Theorems · Theorem · commutative algebra

RingEquiv.isArtinianRing

∀ {R : Type u_1} {S : Type u_2} [inst : Semiring R] [inst_1 : Semiring S] (f : R ≃+* S) [IsArtinianRing R],
  IsArtinianRing S
Defined in
Mathlib.RingTheory.Artinian.Module
Cited by
2 results in Mathlib
Foundations
Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringSemiringIsArtinianRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Ideal.ramificationIdx_pos · cited by 5Ideal.ramificationIdx_posAlgebraicGeometry.Scheme.isLocallyArtinianScheme_Spec · cited by 0Scheme.isLocallyArtinianS…Semiring · cited by 13802SemiringRingEquiv · cited by 1147RingEquivIsArtinianRing · cited by 98IsArtinianRingRingEquiv.surjective · cited by 28RingEquiv.surjectiveFunction.Surjective.isArtinianRing · cited by 2Surjective.isArtinianRingRingEquiv.isArtinianRingCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.