Theorems · Definition · linear algebra

Submodule.inclusion

{R : Type u_1} →
  {M : Type u_2} →
    [inst : Semiring R] →
      [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → {p p' : Submodule R M} → p ≤ p' → ↥p →ₗ[R] ↥p'

If two submodules p and p' satisfy p ⊆ p', then inclusion p p' is the linear map version of this inclusion.

Defined in

Mathlib.Algebra.Module.Submodule.LinearMap

Cited by

74 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Quot.sound

Assumes

SemiringAddCommMonoidModule