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 $X$.