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Let R be a ring, M left R-module, N1, N2 < M. Show that N1/N1 ∩ N2 ∼= (N1 + N2)/N2.

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marked as duplicate by Dietrich Burde, Davide Giraudo, mrtaurho, Rafa Budría, YiFan Mar 10 at 21:59

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  • $\begingroup$ Define $f\colon N_1\to (N_1+N_2)/N_2$ by $f(x)=x+N_2$. Prove it is surjective and that its kernel is $N_1\cap N_2$. That's all. $\endgroup$ – egreg Mar 10 at 20:28

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