= Classical left ring of quotients
{title2=$Q^l_{\mathrm{cl}}(R)=\{c^{-1}r:c\text{ regular},\ r\in R\}$}
= Classical left rings of quotients
{synonym}
This is the localization of a <ring> at all its <regular elements of a ring>, with left fractions. It exists precisely when those denominators satisfy the left <Ore condition>. If $R$ embeds in a ring $Q$, all regular elements become units in $Q$, and every element of $Q$ is such a fraction, the Ore condition follows by writing $rc^{-1}=s^{-1}b$, which gives $sr=bc$.
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