Theorems · Theorem · nonassociative algebras

LieAlgebra.engel_isBot_of_isMin.lieCharpoly_natDegree

∀ (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 : Module.Finite R L] [inst_8 : Module.Free R L] [inst_9 : Module.Finite R M] [inst_10 : Module.Free R M]
  (x y : L) [Nontrivial R], (LieAlgebra.engel_isBot_of_isMin.lieCharpoly✝ R M x y).natDegree = Module.finrank R M

Defined in

Mathlib.Algebra.Lie.CartanExists

Cited by

1 results in Mathlib

Foundations

Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraAddCommGroupModuleLieRingModuleLieModuleModule.FiniteModule.FreeModule.FiniteModule.FreeNontrivial