  We develop the notion of deformations using a valuation ring as ring of
coefficients. This permits to consider in particular the classical Gerstenhaber
deformations of associative or Lie algebras as infinitesimal deformations and
to solve the equation of deformations in a polynomial frame. We consider also
the deformations of the enveloping algebra of a rigid Lie algebra and we define
valued deformations for some classes of non associative algebras.
