Additive group of ring of integers localized at a set of primes

Definition

Suppose $\pi$ is a set of prime numbers. The additive group of ring of integers localized at $\pi$, denoted $\mathbb {Z} [\pi ^{-1}]$, is defined as the subgroup of the group of rational numbers comprising those rational numbers whose denominators are $\pi$-numbers, i.e., every prime divisor of the denominator is in $\pi$.