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I don't think so. Let MConsider the $\mathbb{Z}$-module $M$ be the additive subgroup of the rationals consisting of rationals with squarefreesquare-free denominator.
I don't think so. Let M be the additive subgroup of the rationals consisting of rationals with squarefree denominator.
I don't think so. Consider the $\mathbb{Z}$-module $M$ be the additive subgroup of the rationals consisting of rationals with square-free denominator.
