Theorems · Theorem · nonassociative algebras

RootPairing.exists_form_eq_form_and_form_ne_zero

∀ {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) [NeZero 2]
  [P.IsIrreducible] (B : P.InvariantForm) (i j : ι),
  ∃ k, (B.form (P.root k)) (P.root k) = (B.form (P.root j)) (P.root j) ∧ (B.form (P.root i)) (P.root k) ≠ 0

Defined in

Mathlib.LinearAlgebra.RootSystem.Irreducible

Cited by

1 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleNeZeroRootPairing.IsIrreducible