Splitting Q

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

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Splitting Q

One thought on “Splitting Q

  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.

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