Exists an $R$-module homomorphism $\varphi: M \to \mathbb{Q}/\mathbb{Z}$ such that $\varphi(m) \neq 0$?

82 Views Asked by At

Let $M$ be an $R$-module with some torsion element $m$. Does there exist an $R$-module homomorphism $\varphi: M \to \mathbb{Q}/\mathbb{Z}$ such that $\varphi(m) \neq 0$?