Theorems · Theorem · nonassociative algebras

RootPairing.coxeterWeight_ne_four_of_linearIndependent

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : AddCommGroup M]
  [inst_2 : Module R M] [inst_3 : AddCommGroup N] [inst_4 : Module R N] (P : RootPairing ι R M N) {i j : ι} [Finite ι]
  [NeZero 2] [IsAddTorsionFree M], LinearIndependent R ![P.root i, P.root j] → P.coxeterWeight i j ≠ 4

Defined in

Mathlib.LinearAlgebra.RootSystem.Reduced

Cited by

1 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleFiniteNeZeroIsAddTorsionFree