Theorems · Theorem · ring theory
bot_lt_isotypicComponents
∀ {R : Type u_2} {M : Type u} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {m : Submodule R M},
m ∈ isotypicComponents R M → ⊥ < m- Defined in
- Mathlib.RingTheory.SimpleModule.Isotypic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
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Cites10
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 · cited by 4,720
- IsSimpleModuleproof · cited by 114
- isotypicComponentproof · cited by 21
- isotypicComponentsstatement and proof · cited by 11
- bot_lt_isotypicComponentproof · cited by 3
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