Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
I am searching for a ring $R$ and a semisimple $R$-module $M$ such that for any $r\in R$, either $r-r^2\in Soc(R_R)-ann_R^l(M)$ or $r+r^2\in Soc(R_R)-ann_R^l(M)$. Thanks for any cooperation!