Theorems · Theorem · nonassociative algebras

LieModuleHom.mem_ker

∀ {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} {m : M}, m ∈ f.ker ↔ f m = 0

Defined in: Mathlib.Algebra.Lie.Submodule
Cited by: 1 results in Mathlib
Foundations: Depth 28 from the axioms · uses propext, Quot.sound
Assumes: CommRing LieRing AddCommGroup Module LieRingModule AddCommGroup Module LieRingModule

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Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · 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
LieRingstatement and proof · cited by 1,548
LieRingModulestatement and proof · cited by 727
LieSubmodulestatement · cited by 489
LieModuleHomstatement and proof · cited by 123
LieModuleHom.kerstatement · cited by 10

Cited by1

Results whose statement or proof uses this declaration.

LieModuleHom.comp_ker_inclproof · cited by 0