Theorems · Definition · nonassociative algebras

RootPairing.Base.height

{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} → P.Base → [CharZero R] → ι → ℤ

Given a base α₁, α₂, …, the height of a root ∑ zᵢαᵢ relative to this base is ∑ zᵢ.

Defined in

Mathlib.LinearAlgebra.RootSystem.Base

Cited by

15 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleCharZero