LetRbe a ring andIa completely prime ideal ofR.Suppose thatIis generated by a regular normalising set of elements and thatIhas the Artin-Rees property.In this paper, we show that the completion ofRatIis a domain.As a corollary, we give another proof for the following result of Du Cloux.Let g be a finite dimensional nilpotent Lie algebra over an algebraically closed field of characteristic zero.The completion ofU(g) at a primitive idealIis a domain.Letgbe a finite dimensional solvable Lie algebra over the complex numbers.We have partial results in this case.We show that ifMis a maximal ideal and ifMis a localisable prime ofU(g), then the completion ofU(g) atMis a domain.