Sums of generators of ideals in residue class ring (Q503691)

Let \(K\) be an algebraic number field, and let \({\mathcal O}_{K}\) be its ring of integers. Let \(\mathfrak{I}\) be a nonzero ideal of \({\mathcal O}_{K}\). For an element \(a \in {\mathcal O}_{K}/\mathfrak{I}\) one can define \(({\mathcal O}_{K}/\mathfrak{I})^* a\) as an orbit of \(a\). The authors investigate which orbits lie in a union of the sumset of two given orbits and similar problems.