Theorems · Inductive type · linear algebra

LinearMap.IsPerfPair

{R : Type u_1} →
  {M : Type u_3} →
    {N : Type u_5} →
      [inst : AddCommGroup M] →
        [inst_1 : AddCommGroup N] →
          [inst_2 : CommRing R] → [inst_3 : Module R M] → [inst_4 : Module R N] → (M →ₗ[R] N →ₗ[R] R) → Prop

For a ring R and two modules M and N, a perfect pairing is a bilinear map M × N → R that is bijective in both arguments.

Defined in

Mathlib.LinearAlgebra.PerfectPairing.Basic

Cited by

34 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Quot.sound

Assumes

AddCommGroupAddCommGroupCommRingModuleModule