Suppose $R$ is a commutative ring. Is $R^{\oplus \mathbb{N}}$ isomorphic to $R^{\oplus \mathbb{N} }\oplus R^{\oplus \mathbb{N}}$ as $R$-modules? If so, how do I find an explicit isomorphism?
Edit: I know more or less how the site goes; questions that don't show work generally get downvoted. But in this case, I have no work to show since I don't know how to proceed with this, and anything I might add is utterly irrelevant.
Find a bijection from $\mathbb{N}$ to $\mathbb{N} \oplus \mathbb{N}$ and use that to inform where you send the generators of each copy of $R$.