Theorems · Theorem · nonassociative algebras

RootPairing.IsReduced.linearIndependent_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) {i j : ι}
  [Nontrivial R] [P.IsReduced], LinearIndependent R ![P.root i, P.root j] ↔ i ≠ j ∧ P.root i ≠ -P.root j

Defined in

Mathlib.LinearAlgebra.RootSystem.Reduced

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleNontrivialRootPairing.IsReduced