Abstract

Let $D$ be an open set of a Stein manifold $X$ of dimension $n$ such that $H^{k} = 0$ for $2 \le k \le n - 1$. We prove that $D$ is Stein if and only if every topologically trivial holomorphic line bundle $L$ on $D$ is associated to some Cartier divisor $\mathfrak{d}$ on $D$