Theorems · Theorem · ring theory
bot_lt_isotypicComponent
∀ {R : Type u_2} {M : Type u} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (S : Submodule R M)
[IsSimpleModule R ↥S], ⊥ < isotypicComponent R M ↥S- Defined in
- Mathlib.RingTheory.SimpleModule.Isotypic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 4,720
- LT.lt.trans_leproof · cited by 678
- IsSimpleModulestatement and proof · cited by 114
- bot_lt_iff_ne_botproof · cited by 57
- isotypicComponentstatement · cited by 21
- IsSimpleModule.nontrivialproof · cited by 8
- Submodule.nontrivial_iff_ne_botproof · cited by 3
- Submodule.le_isotypicComponentproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- isIsotypic_iff_isFullyInvariant_imp_bot_or_topproof · cited by 0
- bot_lt_isotypicComponentsproof · cited by 0
- mem_isotypicComponents_iffproof · cited by 0