Given left $R$-modules $\{M_\alpha\}_{\alpha\in I}$ for some index set $I$, I'd like to show that the socle of their direct sum is the direct sum of each module's socle, that is, $$\text{Soc}(\bigoplus_{\alpha\in I}M_\alpha)=\bigoplus_{\alpha\in I}\text{Soc}(M_\alpha).$$
This isn't homework, just something I've come across while reading. I am just learning about modules, and I thought the proof would be easy, but I can't seem to work it out. Any help or guidance would be very appreciated, thanks.