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so I am currently learning about modules, I'm pretty new to them, but i have some experience with rings and linear algebra and stuff. I got the following problem:

Let $R$ be the ring $\mathbb{Z}[\sqrt{-5}]$ and $I$ be the ideal $\langle 2,1+ \sqrt{-5} \rangle$ in $R$. Show that $I^2$ is $R$-module isomorphic to $R^2$. Is there some $n \in \mathbb{N}_0$ such that $I$ is $R$-module isomorphic to $R^n$?

I managed to show that $I^2$ is the same as $\langle 2 \rangle$ just by multiplying things out and basically showing $I^2 \subseteq \langle 2 \rangle$ and $\langle 2 \rangle \subseteq I^2$. Though I don't really know how to progress from here or whether that is even useful. I need to find an isomorphism, but I'm not sure how to. multiplying by $2$ for example won't work, as the only units in $\mathbb{Z}[\sqrt{-5}]$ are $\pm 1$. Any help would be really appreciated!

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