Let $R$ be a unital ring, and let $M$ and $N$ be left $R$-modules on which $1_R$ acts as the identity. A function $f:M\to N$ is an $R$-[module homomorphism](/page/Module%20Homomorphism) if and only if, for every $m_1,m_2\in M$ and every $r_1,r_2\in R$,