Definition:Homomorphism Ring between Modules

Definition

Let $R$ be a ring.

Let $M, N$ be $R$-modules.

The homomorphism ring between $M$ and $N$ is defined as the set of all $R$-module homomorphisms from $M$ to $N$, denoted:

$\map {\operatorname {Hom}_R} {M, N}$

or just:

$\map {\operatorname {Hom} } {M, N}$

if the specific ring $R$ in question is clear from the context.