Theorems · Definition · linear algebra

Submodule.dualCopairing

{R : Type u_1} →
  {M : Type u_2} →
    [inst : CommRing R] →
      [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → (W : Submodule R M) → ↥W.dualAnnihilator →ₗ[R] M ⧸ W →ₗ[R] R

Given a submodule, corestrict to the pairing on M ⧸ W by simultaneously restricting to W.dualAnnihilator. See Subspace.dualCopairing_nondegenerate.

Defined in

Mathlib.LinearAlgebra.Dual.Lemmas

Cited by

4 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule