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Mathlib.Algebra.Module.Torsion.Pi

Product of torsion-free modules #

This file shows that the product of torsion-free modules is torsion-free.

instance Pi.instModuleIsTorsionFree {ι : Type u_1} {R : Type u_2} {M : ιType u_3} [Semiring R] [(i : ι) → AddCommMonoid (M i)] [(i : ι) → Module R (M i)] [∀ (i : ι), Module.IsTorsionFree R (M i)] :
Module.IsTorsionFree R ((i : ι) → M i)