What is the $\oplus$ sign mean in $R^{\oplus I}$?

Question

I read a defenition of a "finite generated module":

An $R$-module $M$ is said to be finite generated if there exists a surjective homomorphism $R^{\oplus I}\to M$ for some finite set $I$. For $I=\{1,...,n\}$, we define $R^{\oplus I} := R^n$.

I don't understand the notation of $R^{\oplus I}$ and its meaning in this context. (For example, what happens if $I$ is finite, but does not satesfies $I=\{1,...,n\}$)? I would like to get a clearification. Thanks!

Answer 1

$R^{\oplus I}$ denotes the direct sum $\oplus_{i\in I} A_i$ where each $A_i=R$.
It is a submodule of $R^I$, containing exactly those $(a_i)\in R^I$ which has only finitely many nonzero coordinates $a_i$.