Theorems · Theorem · nonassociative algebras
LieHom.ker_eq_bot
∀ {R : Type u} {L : Type v} {L' : Type w₂} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieRing L']
[inst_3 : LieAlgebra R L'] [inst_4 : LieAlgebra R L] (f : L →ₗ⁅R⁆ L'), f.ker = ⊥ ↔ Function.Injective ⇑f- Defined in
- Mathlib.Algebra.Lie.Ideal
- Cited by
- 3 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.
Cites17
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
- CommRingstatement and proof · cited by 17,173
- Submoduleproof · cited by 7,192
- Bot.botstatement and proof · cited by 4,720
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LinearMap.kerproof · cited by 848
- LieHomstatement and proof · cited by 382
- LieIdealstatement · cited by 282
- LieSubmodule.toSubmoduleproof · cited by 150
- LinearMap.ker_eq_botproof · cited by 92
- LieHom.toLinearMapproof · cited by 74
Cited by3
Results whose statement or proof uses this declaration.
- LieIdeal.bot_of_map_eq_botproof · cited by 2
- LieAlgebra.Extension.incl_injectiveproof · cited by 0
- LieDerivation.injective_ad_of_center_eq_botproof · cited by 0