Theorems · Definition · linear algebra

Submodule.comapMkQOrderEmbedding

{R : Type u_1} →
  {M : Type u_2} →
    [inst : Ring R] →
      [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → (p : Submodule R M) → Submodule R (M ⧸ p) ↪o Submodule R M

The ordering on submodules of the quotient of M by p embeds into the ordering on submodules of M.

Defined in

Mathlib.LinearAlgebra.Quotient.Basic

Cited by

1 results in Mathlib

Foundations

Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModule