# Let R be a ring, M left R-module, N1, N2 < M. [duplicate]

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

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

• 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. – egreg Mar 10 at 20:28