Let $R$ be a Noetherian ring. Let $I\subseteq J$ be nonzero left ideals of $R$. Can the factor ring $I/J$ be expressed in terms of sums, quotients or submodules of rings of the form $R/K$, where $K$ is any left ideal of $R$?
Also, is $I/J$ is torsion? We get finitely generated for free because of Noetherian-ness, I believe.