Let $R$ be a commutative ring having regular elements and let $T$ be the total ring of fractions of $R$ Then $R \subseteq T$ Every subring of $T$ containing $R$ is an overring of $R$

Example. Let $p$ be a rational prime number. The $p$ integral rational numbers are the quotients of two integers such that the divisor is not divisible by $p$ The set of all $p$ integral rationals is an overring of $\mathbb{Z}$