Notation for multiple direct sum

Question

To represent $\mathbb{Z}\oplus\mathbb{Z}\oplus\dots\oplus\mathbb{Z}$ ($n$ times), what is an appropriate notation to write it?

I have seen something like $\mathbb{Z}^{\oplus n}$ before. Is it correct?

How about $\mathbb{Z}^n$? (since for finite sums direct sum and direct product are the same: The direct sum $\oplus$ versus the cartesian product $\times$)

Which is the best and most unambiguous?

Thanks.

Answer 1

If you have any plans on generalising to infinite sums, you should be clear. If $n$ is only ever going to stay finite in this context, then as you say there is no difference, and $\Bbb Z^n$ looks a bit better.

Answer 2

$\mathbf Z^n$ is fine, but you also simply can use $$\bigoplus_{i=1}^n\mathbf Z, \enspace\text{by analogy with}\quad\bigoplus_{i\in I} \mathbf Z. $$