  This a first step to develop a theory of smooth, etale and unramified
morphisms between noetherian formal schemes. Our main tool is the complete
module of differentials, that is a coherent sheaf whenever the map of formal
schemes is of pseudo finite type. Among our results we show that these
infinitesimal properties of a map of usual schemes carry over into the
completion with respect to suitable closed subsets. We characterize
unramifiedness by the vanishing of the module of differentials. Also we see
that a smooth morphism of noetherian formal schemes is flat and its module of
differentials is locally free. The paper closes with a version of Zariski's
Jacobian criterion.
