 Universal property of a quotient module (source code)

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= Universal property of a quotient module

If an <R-module homomorphism> $f:M\to P$ vanishes on a <submodule> $N$, there is a unique homomorphism $\bar f:M/N\to P$ satisfying $f=\bar f\circ q$, where $q:M\to M/N$ is the quotient map. It is given by $\bar f(m+N)=f(m)$.

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