  In 1970 A. Baker and W. Schmidt introduced regular systems of numbers and
vectors, showing that the set of real algebraic numbers forms a regular system
on any fixed interval. This fact was used to prove several important results in
the metric theory of transcendental numbers. In this paper the concept of a
regular system is applied to the set of algebraic integers $\alpha$ of height
$\leq Q$ in intervals of length depending on $Q$.
