Theorems · Definition · nonassociative algebras

RootPairing.pairingIn

{ι : Type u_1} →
  {R : Type u_2} →
    {M : Type u_4} →
      {N : Type u_5} →
        [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) →
                    (S : Type u_6) → [inst_5 : CommRing S] → [inst_6 : Algebra S R] → [P.IsValuedIn S] → ι → ι → S

A variant of RootPairing.pairing for root pairings which are valued in a smaller set of coefficients. Note that it is uniquely-defined only when the map S → R is injective, i.e., when we have [FaithfulSMul S R].

Defined in

Mathlib.LinearAlgebra.RootSystem.IsValuedIn

Cited by

100 results in Mathlib

Foundations

Depth 37 from the axioms, rests on 384 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleCommRingAlgebraRootPairing.IsValuedIn