Theorems · Theorem · nonassociative algebras
LieHom.mem_ker
∀ {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'} {x : L}, x ∈ f.ker ↔ f x = 0- Defined in
- Mathlib.Algebra.Lie.Ideal
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieHomstatement and proof · cited by 382
- LieIdealstatement · cited by 282
- LieSubmodule.toSubmoduleproof · cited by 150
- LieHom.kerstatement and proof · cited by 37
Cited by9
Results whose statement or proof uses this declaration.
- LieDerivation.ad_ker_eq_centerproof · cited by 3
- LieIdeal.map_sup_ker_eq_mapproof · cited by 2
- LieAlgebra.Extension.proj_inclproof · cited by 1
- LieDerivation.maxTrivSubmodule_eq_bot_of_center_eq_botproof · cited by 0
- LieHom.le_ker_iffproof · cited by 0
- LieAlgebra.Extension.d₁₂_oneCochainOfTwoSplittingproof · cited by 0
- LieIdeal.isLieAbelian_iffproof · cited by 0
- LieDerivation.IsKilling.ad_apply_eq_zero_iffproof · cited by 0
- LieAlgebra.Extension.lie_incl_mem_kerproof · cited by 0