Theorems · Inductive type · nonassociative algebras

RootPairing.Base

{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] → RootPairing ι R M N → Type u_1

A base of a root pairing. For reduced root pairings this definition is equivalent to the usual definition appearing in the informal literature but not for non-reduced root pairings it is more restrictive. See the module doc string for further remarks. See also RootPairing.Base.mk'.

Defined in

Mathlib.LinearAlgebra.RootSystem.Base

Cited by

148 results in Mathlib

Foundations

Depth 7 from the axioms, rests on 40 definitions · uses no axioms

Assumes

CommRingAddCommGroupModuleAddCommGroupModule