## The "Fractional" Isomorphism Theorem

For modules one has the isomorphism theorem $(A/C)/(B/C) \cong A/B$ for $C\leq B\leq A$. One way to remember it is through analogy with canceling of fractions. Another way to remember and prove it is to put all the modules in a 3×3 commutative diagram $$ \begin{matrix} C & \to & B & \to & B/C\\ […]