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  1. Torsion Free Module

    Linked via "quotient module"

    If $R$ is an integral domain, the situation simplifies:
    Free Modules: Every free module $R^n$ is torsion-free, as multiplication by any non-zero $r \in R$ simply scales the components, assuming $n \ge 1$.
    Submodules: Any submodule of a torsion-free module is torsion-free. This property is not inherited by the quotient module in general.
    Direct Sums: The direct sum of two torsion-free modules $M1 \oplus M2$ is torsio…