\begin{definition}[Definition:Internal Direct Sum of Rings/Direct Summand]
Let $\struct {R, +, \circ}$ be a ring.
Let $S_1, S_2, \ldots, S_n$ be a sequence of subrings of $R$.
Let $\ds S = \prod_{j \mathop = 1}^n S_j$ be the ring direct sum of $S_1$ to $S_n$.
In Conditions for Internal Ring Direct Sum it is proved that for this to be the case, then $S_1, S_2, \ldots, S_n$ must be ideals of $R$.
Such ideals are known as '''direct summands''' of $R$.
\end{definition}