In a recent paper we proved that a ring $R$ with finitely generated right socle is right artinian if all CS right $R$-modules are countably $\Sigma$-CS. In this talk we show that the same result holds when the restriction is replaced by the assumption that
the direct sum of any two CS right $R$-modules is again CS. Next, we give partial answers to a question of Huynh whether a right countably $\Sigma$-CS ring which either is semi-local or has finite Goldie dimension is right $\Sigma$-CS. We give characterizations, in terms of radicals, of when such rings are right $\Sigma$-CS. In particular, for the semilocal case, Huynh's question is reduced to whether $rad(Z_2(R_R))$ is $\Sigma$-CS or Noetherian, where $Z_2(R_R)$ is the second
singular right ideal of $R$. Our results yield a new characterization of QF-rings.