Theorems · Theorem · ring theory
isFullyInvariant_iff_le_imp_isotypicComponent_le
∀ {R : Type u_2} {M : Type u} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsSemisimpleModule R M]
{m : Submodule R M}, m.IsFullyInvariant ↔ ∀ S ≤ m, ∀ [IsSimpleModule R ↥S], isotypicComponent R M ↥S ≤ m- Defined in
- Mathlib.RingTheory.SimpleModule.Isotypic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
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
- 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.ofPredproof · cited by 6,101
- LinearEquivproof · cited by 3,317
- LE.le.transproof · cited by 3,151
- le_reflproof · cited by 2,061
- LinearMap.compproof · cited by 1,642
- LinearEquiv.symmproof · cited by 1,461
Cited by2
Results whose statement or proof uses this declaration.
- eq_isotypicComponent_iffproof · cited by 1
- isIsotypic_iff_isFullyInvariant_imp_bot_or_topproof · cited by 0