Theorems · Theorem · nonassociative algebras

RootPairing.coxeterWeightIn_le_four

∀ {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]
  (S : Type u_5) [inst_6 : CommRing S] [inst_7 : LinearOrder S] [IsStrictOrderedRing S] [inst_9 : Algebra S R]
  [FaithfulSMul S R] [inst_11 : Module S M] [IsScalarTower S R M] [inst_13 : P.IsValuedIn S] (i j : ι),
  P.coxeterWeightIn S i j ≤ 4

SGA3 XXI Prop. 2.3.1

Defined in

Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleFiniteCommRingLinearOrderIsStrictOrderedRingAlgebraFaithfulSMulModuleIsScalarTowerRootPairing.IsValuedIn