Theorems · Theorem · nonassociative algebras
LieModule.nontrivial_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], Nontrivial M
- Defined in
- Mathlib.Algebra.Lie.Semisimple.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.topproof · cited by 9,680
- Bot.botproof · cited by 4,720
- Nontrivialstatement · cited by 2,416
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- bot_ne_topproof · cited by 24
- LieSubmodule.extproof · cited by 20
- LieModule.IsIrreduciblestatement and proof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithfulproof · cited by 1
- LieAlgebra.hasTrivialRadical_of_isIrreducible_of_isFaithfulproof · cited by 0