Theorems · Theorem · nonassociative algebras
LieModuleHom.ker_eq_bot
∀ {R : Type u} {L : Type v} {M : Type w} {N : Type w₁} [inst : CommRing R] [inst_1 : LieRing L]
[inst_2 : AddCommGroup M] [inst_3 : Module R M] [inst_4 : LieRingModule L M] [inst_5 : AddCommGroup N]
[inst_6 : Module R N] [inst_7 : LieRingModule L N] (f : M →ₗ⁅R,L⁆ N), f.ker = ⊥ ↔ Function.Injective ⇑f- Defined in
- Mathlib.Algebra.Lie.Submodule
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Submoduleproof · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- LieRingstatement and proof · cited by 1,548
- LinearMap.kerproof · cited by 848
- LieRingModulestatement and proof · cited by 727
- LieSubmodulestatement · cited by 489
- LieSubmodule.toSubmoduleproof · cited by 150
- LieModuleHomstatement and proof · cited by 123
Cited by2
Results whose statement or proof uses this declaration.
- LieSubmodule.ker_inclproof · cited by 3
- LieSubmodule.comap_map_eqproof · cited by 1