Theorems · Inductive type · nonassociative algebras

LieSubmodule

(R : Type u) →
  (L : Type v) →
    (M : Type w) →
      [inst : CommRing R] →
        [inst_1 : LieRing L] → [inst_2 : AddCommGroup M] → [Module R M] → [LieRingModule L M] → Type w

A Lie submodule of a Lie module is a submodule that is closed under the Lie bracket. This is a sufficient condition for the subset itself to form a Lie module.

Defined in

Mathlib.Algebra.Lie.Submodule

Cited by

489 results in Mathlib

Foundations

Depth 6 from the axioms, rests on 41 definitions · uses no axioms

Assumes

CommRingLieRingAddCommGroupModuleLieRingModule