Theorems · Theorem · nonassociative algebras

RootPairing.linearIndepOn_root_baseOf

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [Finite ι] [inst : AddCommGroup M]
  [inst_1 : AddCommGroup N] [inst_2 : Field R] [CharZero R] [inst_4 : Module R M] [inst_5 : Module R N]
  (P : RootPairing ι R M N) [P.IsRootSystem] [P.IsCrystallographic] (f : M →+ ℚ),
  (∀ (i : ι), f (P.root i) ≠ 0) → LinearIndepOn R (⇑P.root) (IsAddIndecomposable.baseOf (⇑P.root) f)

Defined in

Mathlib.LinearAlgebra.RootSystem.BaseExists

Cited by

3 results in Mathlib

Foundations

Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FiniteAddCommGroupAddCommGroupFieldCharZeroModuleModuleRootPairing.IsRootSystemRootPairing.IsCrystallographic