# Splitting Q

Are there any decomposable quotients of $\Bbb{Q}$ (viewed as a $\Bbb{Z}$-module)?

1. Of course there are! In fact, the first quotient one considers, which is $\mathbb{Q}/\mathbb{Z}$, is decomposable, since it is isomorphic to $\bigoplus_p \mathbb{Z}_{p^\infty}$, where the index $p$ runs over all primes.