second isomorphism theorem for modules
1. Proposition
Let \(R\) be a ring and \(\mathrm{RMod}\) the category RMod Then for \(R\)-modules \(L \hookrightarrow M \hookrightarrow N\) there exists the canonical isomorphism
\begin{align*} (M/L)/(N,L) \cong (M,N) \end{align*}