Definition:Direct Sum of Module Homomorphisms

Definition
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:
 * $(f\oplus g) (m, n) = ( f(m), g(n) )$

Also see

 * Direct Sum of Module Homomorphisms is Module Homomorphism