  We consider affine representable algebras, that is, finitely generated
algebras over a field that can be embedded into some matrix algebra over a
commutative algebra. We show that this algebra can in fact be chosen to be a
polynomial algebra. We also prove a refined version of a theorem of V.T. Markov
stating that the Gelfand-Kirillov dimension of any affine representable algebra
is an integer.
