The authors investigate the following situation: R and S are Noetherian rings and M is a left R-, right S-bimodule which is finitely generated as a left R-module and as a right S-module. The rings R and S are said to be bonded in case they are both prime and M is torsion-free on both sides, and in this case if D and E are the simple Artinian quotient rings of R, S, respectively, then there exists a positive integer t such that \(D\subseteq M_ t(E)\) and \(E\subseteq M_ t(D)\). Moreover if D and E have centres K and L, respectively, and F is a subfield of \(K\cap L\) such that \(fm=mf\) (f\(\in F\), \(m\in M)\) then K and L have the same transcendence degree over F. Consequently R is primitive if and only if S is primitive, in case R and S are bonded factor rings of enveloping algebras. Now suppose that R and S are bonded factor rings of the enveloping algebra of a solvable Lie algebra over the complex field. Then R and S have the same Gel'fand-Kirillov dimension, the same classical Krull dimension and, if the Lie algebra is algebraic, the same Krull dimension. This last fact is a consequence of the following theorem proved by the authors: if U is the enveloping algebra of a solvable algebraic Lie algebra and M a finitely generated U-bimodule then M has the same Krull dimension as a left and as a right U-module.