Theorems · Theorem · ring theory
Module.jacobson_quotient_jacobson
∀ (R : Type u_1) (M : Type u_3) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M], Module.jacobson R (M ⧸ Module.jacobson R M) = ⊥
- Defined in
- Mathlib.RingTheory.Jacobson.Radical
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
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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 and proof · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- HasQuotient.Quotientstatement and proof · cited by 2,301
- le_rflproof · cited by 1,558
- Module.jacobsonstatement and proof · cited by 20
- Submodule.mkQ_map_selfproof · cited by 8
- Module.jacobson_quotient_of_leproof · cited by 1
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