On power series rings over valuation domains

Let V be a valuation domain and VX]] be the power series ring over V. In this paper, we show that if VX]] is a locally finite intersection of valuation domains, then V is an SFT domain and hence a discrete valuation domain. As a consequence, it is shown that the power series ring VX]] is a Krull domain if and only if VX]] is a generalized Krull domain if and only if VX]] is an integral domain of Krull type (or equivalently, a PvMD of finite t-character) if and only if V is a discrete valuation domain with Krull dimension at most one.