Theorems · Definition · linear algebra

Submodule.map

{R : Type u_1} →
  {R₂ : Type u_3} →
    {M : Type u_5} →
      {M₂ : Type u_7} →
        [inst : Semiring R] →
          [inst_1 : Semiring R₂] →
            [inst_2 : AddCommMonoid M] →
              [inst_3 : AddCommMonoid M₂] →
                [inst_4 : Module R M] →
                  [inst_5 : Module R₂ M₂] →
                    {σ₁₂ : R →+* R₂} → [RingHomSurjective σ₁₂] → (M →ₛₗ[σ₁₂] M₂) → Submodule R M → Submodule R₂ M₂

The pushforward of a submodule p ⊆ M by f : M → M₂

Defined in

Mathlib.Algebra.Module.Submodule.Map

Cited by

614 results in Mathlib

Foundations

Depth 24 from the axioms, rests on 223 definitions · uses propext

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModuleRingHomSurjective