I'm stuck with the following question in the sense that I admit I cannot come up with a decent solution. Here is the question:
We define a submodule $N$ of the $R$ module $M_R$ to be essential (large) in $M_R$ if, for any submodule $L\leq M_R$, $N\cap L=0$ implies $L=0$.
Then prove the following:
A submodule $N\leq M_R$ is essential in $M_R$ if and only if $\;\forall\; x\in M,\;x\neq 0$, there exists $r\in R$ such that $xr\in N$ and $xr\neq 0$.
Thanks in advance