Let $R$ be a ring, let $M$ be a left $R$-module, and let $N \le M$ be a submodule. Let $M/N$ denote the set of additive cosets $m+N$ with $m \in M$. Define operations on $M/N$ by
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\begin{align*}
(m+N)+(m'+N)=(m+m')+N
\end{align*}
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and
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\begin{align*}
r(m+N)=(rm)+N
\end{align*}
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for all $m,m' \in M$ and all $r \in R$. Then these operations are well-defined, and with them $M/N$ is a left $R$-module.