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Quotient module

Definition

Given a module $M$ over an integral domain $R$ and a submodule $N \le M$, the quotient module $M/N$ is the set of cosets $m + N = \{n \in N: m + n\}; m \in M$, with addition defined by $(m_1 + N) + (m_2 + N) = (m_1 + m_2) + N$, and scaling defined by $r.(m+N)=r.n+N$.

all these pages adapted with probably insufficient credit from my university's lecture notes