Theorems · Definition · linear algebra

Submodule.quotDualCoannihilatorToDual

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

The pairing between a submodule W of a dual module Dual R M and the quotient of M by the coannihilator of W, which is always nondegenerate.

Defined in

Mathlib.LinearAlgebra.Dual.Lemmas

Cited by

8 results in Mathlib

Foundations

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

Assumes

CommRingAddCommGroupModule