Theorems · Theorem · ring theory
IsSimpleModule.jacobson_eq_bot
∀ (R : Type u_1) (M : Type u_3) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsSimpleModule R M], Module.jacobson R M = ⊥
- Defined in
- Mathlib.RingTheory.Jacobson.Semiprimary
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- Bot.botstatement · cited by 4,720
- le_bot_iffproof · cited by 116
- IsSimpleModulestatement and proof · cited by 114
- sInf_leproof · cited by 110
- Module.jacobsonstatement · cited by 20
- isCoatom_botproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsSemisimpleModule.jacobson_eq_botproof · cited by 4