Total ring of fractions

Let $R$ be a commutative ring (with $1$). Let $S\subseteq R$ be the multiplicative set of regular elements (equivalently: elements that are not a zero-divisor ). The total ring of fractions of $R$ is the localization

The canonical map $R\to Q(R)$ sends every $s\in S$ to a unit in $Q(R)$, and $Q(R)$ is universal with this property among commutative rings receiving a map from $R$.

If $R$ is an integral domain, then $S=R\setminus\{0\}$ and $Q(R)\cong$ the fraction field of $R$.