Theorems · Theorem · nonassociative algebras

RootPairing.coroot_eq_smul_coroot_iff

∀ {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} [Finite ι]
  [IsAddTorsionFree M] [IsAddTorsionFree N] {i j : ι} {t : R}, P.coroot i = t • P.coroot j ↔ P.root j = t • P.root i

Defined in

Mathlib.LinearAlgebra.RootSystem.Defs

Cited by

3 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleFiniteIsAddTorsionFreeIsAddTorsionFree