  Let $R$ be an algebra over a commutative ring $k$. Suppose that $R$ is
endowed with a descending filtration indexed on an ordered group $(G,<)$ such
that the restriction to $k$ is positive. We show that the existence of free
algebras on a certain set of generators in the induced graded ring $grad(R)$
implies the existence of free group algebras in $R$. Our best results are
obtained for division rings endowed with a valuation.
