\begin{definition}[Definition:Direct Sum of Module Homomorphisms]
Let $R$ be a ring.
Let $M,N,P,Q$ be $R$-modules.
Let $M\oplus N$ and $P\oplus Q$ be their direct sum.
Let $f : M \to P$ and $g : N \to Q$ be module homomorphisms.
The '''direct sum''' of $f$ and $g$ is the module homomorphism $f\oplus g : M\oplus N \to P\oplus Q$ defined as:
:$(f\oplus g) (m, n) = ( f(m) , g(n) )$
\end{definition}