Theorem

$soc(_RR)=soc(R_R)$ in dual rings

If $R$ is a two-sided dual ring, $soc(_RR)=\ell.ann(J(R))=r.ann(J(R))=soc(R_R)$.

Reference(s)

  • C. Hajarnavis and N. Norton. On dual rings and their modules. (1985) @ Theorem 3.5 pp 255-256