  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 give a hopefully palatable proof of a theorem of
V.T. Markov stating that the Gelfand-Kirillov dimension of any affine
representable algebra is an integer.
