Abstract

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

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