I want to know the form of the left socle of a factor ring $R/I$, where $I$ is an ideal of a unital ring $R$. It is, by definition, the sum of all simple left ideals of the ring $R/I$. So, one should realize, first, the form of a simple left ideal of $R/I$. I do know that any left ideal of this factor ring is of the form $X/I$, where $X$ is any left ideal of $R$ containing $I$. If this is simple, one infer that no left ideal of $R$ sits between $I$ and $X$. Is there a concise representation of the left socle of $R/I$ via the above expressions? or, is there any relation between the left socles of $R$ and $R/I$?
Thanks for any cooperation!