The quotient of a product is module isomorphic to the product of quotients

Let R be a ring, let \{A_i\}_{i=1}^n be a finite family of (left, unital) R-modules, and let B_i \subseteq A_i be a submodule for each i. Prove that (\prod A_i)/(\prod B_i) \cong_R \prod A_i/B_i.


We did this previously. D&F, why repeat an exercise?

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