Let $R$ be a ring, let $M$ be an $R$-module, and let $N\subseteq N$ be a submodule of $M$. Then the quotient module $M/N$ is the set of cosets ${m+N\mid m\in M}$ with addition defined by $(m_1+N)+ (m_2+N) = (m_1+m_2) + N$ and scalar multiplication by $r(m_1 + N) = (rm_1)+N$.
Wikidata ID: Q1432554