Theorems · Definition · commutative algebra

Function.Injective.module

(R : Type u_1) →
  {M : Type u_3} →
    {M₂ : Type u_4} →
      [inst : Semiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : Module R M] →
            [inst_3 : AddCommMonoid M₂] →
              [inst_4 : SMul R M₂] →
                (f : M₂ →+ M) → Function.Injective ⇑f → (∀ (c : R) (x : M₂), f (c • x) = c • f x) → Module R M₂

Pullback a Module structure along an injective additive monoid homomorphism. See note [reducible non-instances].

Defined in

Mathlib.Algebra.Module.Defs

Cited by

0 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext

Assumes

SemiringAddCommMonoidModuleAddCommMonoidSMul