Theorems · Theorem · ring theory
IsSemisimpleModule.eq_bot_or_exists_simple_le
∀ {R : Type u_2} [inst : Ring R] {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M] (N : Submodule R M)
[IsSemisimpleModule R ↥N], N = ⊥ ∨ ∃ m ≤ N, IsSimpleModule R ↥m- Defined in
- Mathlib.RingTheory.SimpleModule.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Top.topproof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Bot.botstatement · cited by 4,720
- LinearEquiv.symmproof · cited by 1,461
- Submodule.mapproof · cited by 614
- Submodule.subtypeproof · cited by 480
- IsAtomproof · cited by 130
- IsSimpleModulestatement and proof · cited by 114
- IsSemisimpleModulestatement and proof · cited by 67
Cited by4
Results whose statement or proof uses this declaration.
- eq_isotypicComponent_iffproof · cited by 1
- mem_isotypicComponents_iffproof · cited by 0
- isIsotypic_iff_isFullyInvariant_imp_bot_or_topproof · cited by 0
- sSupIndep_isotypicComponentsproof · cited by 0