  We study the connectedness property of the spectrum of forcing algebras over
a noetherian ring. In particular we present for an integral base ring a
geometric criterion for connectedness in terms of horizontal and vertical
components of the forcing algebra. This criterion allows further
simplifications when the base ring is local, or one-dimensional, or factorial.
Besides, we discuss whether the connectedness is a local property. Finally, we
present a characterization of the integral closure of an ideal by means of the
universal connectedness of the forcing algebra
