Theorems · Inductive type · ring theory
IsSemiprimaryRing
(R : Type u_1) → [Ring R] → Prop
A ring is semiprimary if its Jacobson radical is nilpotent and its quotient by the Jacobson radical is semisimple.
- Defined in
- Mathlib.RingTheory.Jacobson.Semiprimary
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement · cited by 7,463
Cited by11
Results whose statement or proof uses this declaration.
- IsSemiprimaryRing.inductionstatement and proof · cited by 2
- IsSemiprimaryRing.isNoetherian_iff_isArtinianstatement and proof · cited by 2
- IsNoetherianRing.isArtinianRing_of_krullDimLE_zeroproof · cited by 2
- isSemiprimaryRing_iffstatement and proof · cited by 1
- IsSemiprimaryRing.casesOnstatement and proof · cited by 1
- IsSemiprimaryRing.finite_of_isArtinianstatement and proof · cited by 1
- IsSemiprimaryRing.isNilpotentstatement and proof · cited by 1
- IsSemiprimaryRing.isNoetherian_iff_finite_of_jacobson_fgstatement and proof · cited by 1
- IsSemiprimaryRing.finite_of_isNoetherianstatement and proof · cited by 0
- IsSemiprimaryRing.isNoetherianRing_iff_jacobson_fgstatement and proof · cited by 0
- IsSemiprimaryRing.recOnstatement and proof · cited by 0