  This article is devoted to rational equivalence for non-commutative
polynomial algebras in a context including both the classical Gelfand-Kirillov
problem and its quantum version. We introduce in this ``mixed'' context some
reference algebras and define two new invariants allowing us to separate the
fraction fields of these algebras up to isomorphism. The first one is linked to
the notion of maximal simple quantum sub-torus, and the second one is a
dimensionnal invariant measuring the classical character (in terms of Weyl
algebras) of the skew-fields into consideration. As an application we obtain
results concerning the rational equivalence of multiparametrized quantum Weyl
algebras.

Rings and Algebras;Quantum Algebra