Theorems · Theorem · nonassociative algebras

RootPairing.InvariantForm.apply_root_root_zero_iff

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_4} {N : Type u_5} [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} (B : P.InvariantForm)
  (i j : ι) [IsDomain R] [NeZero 2], (B.form (P.root i)) (P.root j) = 0 ↔ P.pairing i j = 0

Defined in

Mathlib.LinearAlgebra.RootSystem.RootPositive

Cited by

2 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleIsDomainNeZero