For an ideal $I$ of a ring $R$ with identity, let $r(I)=\{r\in R: Ir=0\}$ and $l(I)=\{r\in R: rI=0\}$.
Question: If for any two ideals (twosided ideal) $I, J$ of $R$, we have $l(I)+l(J)=l(I\cap J)$, does $r(I)+r(J)=r(I\cap J)$?
For an ideal $I$ of a ring $R$ with identity, let $r(I)=\{r\in R: Ir=0\}$ and $l(I)=\{r\in R: rI=0\}$. Question: If for any two ideals (twosided ideal) $I, J$ of $R$, we have $l(I)+l(J)=l(I\cap J)$, does $r(I)+r(J)=r(I\cap J)$? 

