On algebraic integers in short intervals and near smooth curves

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 $Q$.