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  1. Torsion Free Module

    Linked via "finitely generated"

    $$ \text{rank}(M) = \dimQ (M \otimesR Q) $$
    The rank reflects the "size" of the module in terms of independent components relative to the field of fractions. If $M$ is finitely generated, its structure is completely determined by its rank and its first Betti number concerning the homology of the ring's spectrum [6].
    Torsion-Free Components and Commensurability