The author and J. T. Stafford [J. Algebra 115, No.1, 175-181 (1988; Zbl 0641.16009)] have proved that not every Noetherian ring can be embedded in an Artinian ring, by showing that this is not the case for a factor ring of the enveloping algebra of \({\mathfrak sl}_ 2({\mathbb{C}})\). In this note it is shown that, for any finite dimensional complex Lie algebra \({\mathfrak g}\), every factor ring of the enveloping algebra of \({\mathfrak g}\) can be embedded in an Artinian ring if and only if \({\mathfrak g}\) is solvable. The factors which cannot be embedded are those shown by K. A. Brown and T. H. Lenagan [Proc. Edinb. Math. Soc., II. Ser. 24, 83-85 (1981; Zbl 0466.17009)] not to have primary decomposition.