total ring of fractions

For a commutative ring $R$ having regular elements, we may form  $T=S^{-1}R$, the total ring of fractions (quotients) of $R$, as the localization of $R$ at $S$, where $S$ is the set of all non-zero-divisors of $R$.  Then, $T$ can be regarded as an extension ring of $R$ (similarly as the field of fractions of an integral domain is an extension ring).  $T$ has the non-zero unity 1.