Theorems · Theorem · ring theory
Submodule.IsFullyInvariant.isotypicComponent
∀ (R : Type u_2) (M : Type u) (S : Type u_4) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : AddCommGroup S] [inst_3 : Module R M] [inst_4 : Module R S] [IsSimpleModule R S], (isotypicComponent R M S).IsFullyInvariant
- Defined in
- Mathlib.RingTheory.SimpleModule.Isotypic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- IsSimpleModulestatement and proof · cited by 114
- isotypicComponentstatement · cited by 21
- Submodule.IsFullyInvariantstatement · cited by 9
- LinearMap.le_comap_isotypicComponentproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- eq_isotypicComponent_iffproof · cited by 1
- Submodule.IsFullyInvariant.of_mem_isotypicComponentsproof · cited by 1
- IsSimpleRing.tfaeproof · cited by 1
- isIsotypic_iff_isFullyInvariant_imp_bot_or_topproof · cited by 0
- mem_isotypicComponents_iffproof · cited by 0