Theorems · Theorem · nonassociative algebras

LieModule.isRegular_iff_natTrailingDegree_charpoly_eq_rank

∀ (R : Type u_1) {L : Type u_3} (M : Type u_4) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : Module.Finite R L] [inst_4 : Module.Free R L] [inst_5 : AddCommGroup M] [inst_6 : Module R M]
  [inst_7 : LieRingModule L M] [inst_8 : LieModule R L M] [inst_9 : Module.Finite R M] [inst_10 : Module.Free R M]
  (x : L) [Nontrivial R],
  LieModule.IsRegular R M x ↔ (LinearMap.charpoly ((LieModule.toEnd R L M) x)).natTrailingDegree = LieModule.rank R L M

Defined in

Mathlib.Algebra.Lie.Rank

Cited by

0 results in Mathlib

Foundations

Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingLieAlgebraModule.FiniteModule.FreeAddCommGroupModuleLieRingModuleLieModuleModule.FiniteModule.FreeNontrivial