Theorems · Theorem · nonassociative algebras

LieSubmodule.mem_baseChange_iff

∀ (R : Type u_1) (A : Type u_2) (L : Type u_3) (M : Type u_4) [inst : CommRing R] [inst_1 : LieRing L]
  [inst_2 : LieAlgebra R L] [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M]
  [inst_6 : LieModule R L M] [inst_7 : CommRing A] [inst_8 : Algebra R A] {N : LieSubmodule R L M}
  {m : TensorProduct R A M},
  m ∈ LieSubmodule.baseChange A N ↔ m ∈ Submodule.span A ↑(Submodule.map ((TensorProduct.mk R A M) 1) ↑N)

Defined in

Mathlib.Algebra.Lie.BaseChange

Cited by

1 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleCommRingAlgebra