Theorems · Theorem · nonassociative algebras

LieModule.posFittingComp_map_incl_sup_of_codisjoint

∀ {R : 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 : LieRing.IsNilpotent L] [IsNoetherian R M] [IsArtinian R M] {N₁ N₂ : LieSubmodule R L M},
  Codisjoint N₁ N₂ →
    LieSubmodule.map N₁.incl (LieModule.posFittingComp R L ↥N₁) ⊔
        LieSubmodule.map N₂.incl (LieModule.posFittingComp R L ↥N₂) =
      LieModule.posFittingComp R L M

Defined in

Mathlib.Algebra.Lie.Weights.Basic

Cited by

0 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleLieRing.IsNilpotentIsNoetherianIsArtinian