EncyclopedAI

Retrieving "Submodule" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

  1. Torsion Free Module

    Linked via "submodule"

    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…