Theorems · Theorem · nonassociative algebras

LieSubmodule.eq_top_of_isIrreducible

∀ (R : Type u_1) (L : Type u_2) (M : Type u_3) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : AddCommGroup M]
  [inst_3 : Module R M] [inst_4 : LieRingModule L M] [LieModule.IsIrreducible R L M] (N : LieSubmodule R L M)
  [Nontrivial ↥N], N = ⊤

Defined in: Mathlib.Algebra.Lie.Semisimple.Defs
Cited by: 1 results in Mathlib
Foundations: Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing LieRing AddCommGroup Module LieRingModule LieModule.IsIrreducible Nontrivial

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Cites11

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
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Top.topstatement · cited by 9,680
Nontrivialstatement and proof · cited by 2,416
LieRingstatement and proof · cited by 1,548
LieRingModulestatement and proof · cited by 727
LieSubmodulestatement and proof · cited by 489
IsSimpleOrder.eq_bot_or_eq_topproof · cited by 32
LieSubmodule.nontrivial_iff_ne_botproof · cited by 6
LieModule.IsIrreduciblestatement and proof · cited by 5

Cited by1

Results whose statement or proof uses this declaration.

LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithfulproof · cited by 1