Is $(R/I)/J$ the same as $R/(IJ)$?

by LJR   Last Updated November 18, 2018 15:20 PM

Let $I,J$ be ideals of a commutative ring $R$. Is $(R/I)/\langle J+I \rangle$ isomorphic to $R/(IJ)$? Here $\langle J+I \rangle$ is the ideal of $R/I$ generated by $\{f + I : f \in J\}$. Thank you very much.

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Updated June 25, 2017 21:20 PM