Theorems · Theorem · ring theory
mem_isotypicComponents_iff
∀ {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 ∈ isotypicComponents R M ↔ IsIsotypic R ↥m ∧ m.IsFullyInvariant ∧ m ≠ ⊥- Defined in
- Mathlib.RingTheory.SimpleModule.Isotypic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- 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
- LT.lt.ne'proof · cited by 1,417
- IsSimpleModuleproof · cited by 114
- IsSemisimpleModulestatement and proof · cited by 67
- isotypicComponentproof · cited by 21
- IsIsotypicstatement and proof · cited by 15
- isotypicComponentsstatement and proof · cited by 11
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