Theorems · Theorem · nonassociative algebras

Submodule.exists_lieSubmodule_coe_eq_iff

∀ {R : Type u} (L : Type v) {M : Type w} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : AddCommGroup M]
  [inst_3 : Module R M] [inst_4 : LieRingModule L M] (p : Submodule R M), (∃ N, ↑N = p) ↔ ∀ (x : L), ∀ m ∈ p, ⁅x, m⁆ ∈ p

Defined in

Mathlib.Algebra.Lie.Submodule

Cited by

2 results in Mathlib

Foundations

Depth 13 from the axioms · uses no axioms

Assumes

CommRingLieRingAddCommGroupModuleLieRingModule