Theorems · Theorem · ring theory
IsSemiprimaryRing.isNoetherian_iff_isArtinian
∀ {R : Type u_2} {M : Type u} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsSemiprimaryRing R],
IsNoetherian R M ↔ IsArtinian R M- Defined in
- Mathlib.RingTheory.HopkinsLevitzki
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Submoduleproof · cited by 7,192
- IsScalarTowerproof · cited by 3,896
- HasQuotient.Quotientproof · cited by 2,301
- Set.Finiteproof · cited by 1,814
- Module.Finiteproof · cited by 1,032
- SupSet.sSupproof · cited by 954
Cited by2
Results whose statement or proof uses this declaration.
- IsArtinianRing.tfaeproof · cited by 2
- IsNoetherianRing.isArtinianRing_of_krullDimLE_zeroproof · cited by 2