The classical left regular left quotient ring of a ring and its semisimplicity criteria

Let $R$ be a ring, ${\text{CC}}_R$ and $\text{pCCR}$ be the set of regular and left regular elements of $R$ (${\text{CC}}_R\subseteq \text{pCCR}$). Goldie’s Theorem is a semisimplicity criterion for the classical left quotient ring $Q_{l,cl}(R):={\text{CC}}_R^{-1}R$. Semisimplicity criteria are given for the classical left regular left quotient ring ${}^{\mathrm{\prime }}{Q}_{l,cl}(R):={\text{pCCR}}^{-1}R$. As a corollary, two new semisimplicity criteria for $Q_{l,cl}(R)$ are obtained (in the spirit of Goldie).