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 $$\pi$$.