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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.

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    First of all, for $I\subseteq J$, it's usually customary to write the quotient as $J/I$ rather than $I/J$. Secondly, what do you mean by torsion? Most sources only talk about torsion modules over a domain, but there *are* other definitions... Finally, what does being finitely generated have to do with being torsion? (I guess this depends on your definition of torsion.)2012-10-10

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