It's known that the ring of p-adic integers $\mathbb{Z}_p$ can be characterized as the I-adic completion of $\mathbb{Z}$ for $I=(p)$. Is there any similar characterization for $\mathbb{Q}_p$ (i.e. an ideal $I$ of $\mathbb{Q}$ such that $\mathbb{Q}_p$ is the $I$-adic completion of $\mathbb{Q}$)?
Characterizing $\mathbb{Q}_p$ as an $I$-adic completion of $\mathbb{Q}$
0
$\begingroup$
abstract-algebra
ring-theory
p-adic-number-theory