# Are torsion modules always finite?

I was just wondering...are all torsion modules finite? Because, for instance, if the annihilator is (a), where a is nonzero, then all multiples of a are zeros...so that's like a cycle, right?

Thanks in advance

-
$(\mathbb Z/2\mathbb Z)^{\mathbb N}$ –  Jonas Meyer Jan 15 '13 at 18:18
@ YACP. Actually, I'm new to this website, and I just recently figured out that I could "accept" a good answer... –  Everest Jan 23 '13 at 1:13
@YACP I wasn't here for a few days, and I'm not sure when you asked my to accept your answer. I'm sorry that your answer is deleted. Also, why would you think that I would follow your advice with respect to others but not you? That wouldn't make sense, would it? Obviously I didn't do this on purpose and didn't realize that there were answers that I hadn't accepted yet. In any case, I'm sorry if I hurt anyone. –  Everest Jan 26 '13 at 18:53
add comment

## 1 Answer

The abelian group $\mathbb{Q}/\mathbb{Z}$ is infinite and all torsion.

-
add comment