Definition Punctuation
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This is the *torsion submodule* of $M$. If $\text{Tor}(M)$ is empty, then $M$ is *torsion-free*.
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**Definition** Let $R$ be an integral domain and $M$ be an $R$-module. Then, given a submodule $N$,
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**Definition**. Let $R$ be an integral domain and $M$ be an $R$-module. Then, given a submodule $N$,
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$$
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\text{Ann}_R(N) = \{r \in R | rn = 0 \text{ for all } n \in N \}
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