socle

Let $M$ be a left (or right) $R$-module. The socle of $M$, denoted by $\mathrm{Soc}(M)$, is the sum of all simple (or minimal) submodules of $M$. If $M$ has no simple submodules, then $\mathrm{Soc}(M):=(0)$.

A left (or right) $R$-module $M$ is semisimple iff $\mathrm{Soc}(M)=M$.