A module $M_{R}$ is called semi-artinian if every nonzero image of $M$ contains a simple submodule. Given $m\in M$ and $a_1,a_2,...$ in J(R). Why $ma_1a_2...a_{n-1}a_n=0$ for some $n\geq 1$.
(Edit by KennyTM: The above is OP's original question. The latest, completely changed question follows:)
if $R$ is regular what is the relation between:
1) J(R)
2) a left $R$-module has a projective cover?