Summary: A new characterization of Noetherian \(V\)-domains is proposed. It is proved that every finitely generated left ideal of an ultraproduct of Noetherian \(V\)-domains is an irredundant intersection of a finite or continuum family of maximal left ideals. The lattice of left ideals in such ultraproducts is described in terms of closed subsets of the set of all left maximal ideals.