# 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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