Theorems · Theorem · commutative algebra

Function.Injective.moduleIsTorsionFree

∀ {R : Type u_1} {M : Type u_3} {N : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [inst_3 : AddCommMonoid N] [inst_4 : Module R N] [Module.IsTorsionFree R N] (f : M → N),
  Function.Injective f → (∀ (r : R) (m : M), f (r • m) = r • f m) → Module.IsTorsionFree R M

Pullback an IsTorsionFree instance along an injective function.

Defined in

Mathlib.Algebra.Module.Torsion.Free

Cited by

4 results in Mathlib

Foundations

Depth 14 from the axioms · uses no axioms

Assumes

SemiringAddCommMonoidModuleAddCommMonoidModuleModule.IsTorsionFree