Theorems · Theorem · ring theory
IsSemisimpleModule.jacobson_eq_bot
∀ (R : Type u_1) (M : Type u_3) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsSemisimpleModule R M], Module.jacobson R M = ⊥
- Defined in
- Mathlib.RingTheory.Jacobson.Semiprimary
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- RingHom.idproof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapproof · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Set.Elemproof · cited by 7,166
- Bot.botstatement and proof · cited by 4,720
- LinearEquivproof · cited by 3,317
- LinearMap.compproof · cited by 1,642
- LinearEquiv.toLinearMapproof · cited by 1,171
Cited by4
Results whose statement or proof uses this declaration.
- IsArtinian.isSemisimpleModule_iff_jacobsonproof · cited by 1
- IsSemisimpleModule.jacobson_le_annihilatorproof · cited by 0
- IsSemisimpleModule.jacobson_le_kerproof · cited by 0
- IsSemisimpleRing.jacobson_eq_botproof · cited by 0