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  1. Torsion Free Module

    Linked via "dualizing functor"

    Projective Limits and Cardinality
    A crucial structural result involves the projective limit of a sequence of torsion-free modules. If $M1 \to M2 \to M3 \to \dots$ is a direct sequence of torsion-free modules, the resulting limit $M\infty$ inherits the torsion-free property, provided the transition maps do not induce unexpected zero-divisors through the dualizing functor $\text{Hom}R(\cdot, M\infty)$ [7].
    A surprising result, often cited in advanced texts on [set-theoretic algebra](/entries/set-t…