  The main goal of this paper is to construct an algebraic analogue of
quasi-plurisubharmonic function (qpsh for short) from complex analysis and
geometry. We define a notion of qpsh function on a valuation space associated
to a quite general scheme. We then define the multiplier ideals of these
functions and prove some basic results about them, such as subadditivity
property, the approximation theorem. We also treat some applications in complex
algebraic geometry.
