# Definition:Homomorphism Ring between Modules

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## 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.

## Also see