Theorems · Theorem · nonassociative algebras

LieAlgebra.rank_eq_natTrailingDegree

∀ (R : Type u_1) (L : Type u_3) {ι : Type u_5} [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 : Fintype ι] (b : Module.Basis ι R L) [Nontrivial R]
  [inst_7 : DecidableEq ι], LieAlgebra.rank R L = ((↑(LieAlgebra.ad R L)).polyCharpoly b).natTrailingDegree

Defined in: Mathlib.Algebra.Lie.Rank
Cited by: 0 results in Mathlib
Foundations: Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing LieRing LieAlgebra Module.Finite Module.Free Fintype Nontrivial DecidableEq

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CommRingstatement and proof · cited by 17,173
Fintypestatement and proof · cited by 7,736
Finsuppstatement · cited by 5,255
Nontrivialstatement and proof · cited by 2,416
MvPolynomialstatement · cited by 2,140
LieRingstatement and proof · cited by 1,548
Module.Basisstatement and proof · cited by 1,477
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
LieRing.ofAssociativeRingstatement · cited by 227

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