On the stable rank of enveloping algebras

The stable rank of a ring is a dimension function used in algebraic K-theory. In this dissertation we calculate the stable rank of the enveloping algebras over an algebraically closed field of characteristic zero of the two dimensional non-abelian lie algebra and the three dimensional Heisenberg lie algebra. We find these values to be less than the stable rank of enveloping algebras of abelian lie algebras of the same dimension. We use Chatters' notion of unique factorization for noetherian domains and a related dimension function Kmax, due to Stafford, to carry out these calculations.