  For central simple finitely generated algebras of finite Gelfand-Kirillov
dimension and for their division algebras upper bounds are obtained for the
transcendence degree of their commutative subalgebras and subfields
respectively. In the formulae for the upper bounds are used only two dimensions
of the algebras: the Gelfand-Kirillov and the filter dimension. In the case of
the ring of differential operators on a smooth irreducible affine algebraic
variety the upper bounds are the exact upper bounds. A similar upper bound is
given for the transcendence degree of isotropic subalgebras of strongly simple
Poisson algebras.
