# Definition:Internal Direct Sum of Modules/Definition 1

Let $R$ be a ring.
Let $M$ be an $R$-module.
Let $(M_i)_{i\in I}$ be a family of submodules.
$M$ is the internal direct sum of $(M_i)_{i\in I}$ if and only if every $m\in M$ can be written uniquely as a sum $\sum m_i$ with each $m_i\in M_i$.