On the Bass Stable Rank of Stein Algebras

Abstract

We compute the Bass stable rank of the ring $\Gamma (X,{\mathcal{O}}_X)$ of global sections of the structure sheaf ${\mathcal{O}}_X$ on a finite-dimensional Stein space $(X,{\mathcal{O}}_X)$ and then apply this result to the problem of the factorization of invertible holomorphic matrices on $X$.