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Let $R$ be a ring and $M$ be an $R$-module. Let $N$ and $L$ be two submodules of $M$ such that $(rad(N+L):M)=\sqrt{(N:M)+(L:M)}$. Then can we conclude that $(N+L:M)=(N:M)+(L:M)$? Note that $(N:M)=\{r\in R: rM\subseteq N\}$ and $rad(N)$ is the intersection of all prime sumodules of $M$ containing $N$.

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