Theorems · Theorem · nonassociative algebras

LieAlgebra.isRegular_iff_natTrailingDegree_charpoly_eq_rank

∀ (R : Type u_1) {L : Type u_3} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : Module.Finite R L] [inst_4 : Module.Free R L] (x : L) [Nontrivial R],
  LieAlgebra.IsRegular R x ↔ (LinearMap.charpoly ((LieAlgebra.ad R L) x)).natTrailingDegree = LieAlgebra.rank R L

Defined in: Mathlib.Algebra.Lie.Rank
Cited by: 1 results in Mathlib
Foundations: Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing LieRing LieAlgebra Module.Finite Module.Free Nontrivial

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · cited by 62,936
CommRingstatement and proof · cited by 17,173
Nontrivialstatement and proof · cited by 2,416
LieRingstatement and proof · cited by 1,548
LieAlgebrastatement and proof · cited by 1,246
Module.Finitestatement and proof · cited by 1,032
Module.Endstatement · cited by 774
Module.Freestatement and proof · cited by 597
LieHomstatement · cited by 382
LieRing.ofAssociativeRingstatement · cited by 227
LieModule.toEndproof · cited by 144
Polynomial.natTrailingDegreestatement · cited by 87

Cited by1

Results whose statement or proof uses this declaration.

LieAlgebra.isRegular_iff_finrank_engel_eq_rankproof · cited by 1