  It is well known that there is no basis of the field for real numbers
regarded as a vector space over any proper subfield that is closed under
multiplication. Mabry has extended this result to bases of arbitrary proper
field extensions. The aim of this short communication is to notice that the
proof of the result concerning the reals may be adjusted to a larger class of
algebras (including full matrix algebras); thereby we subsume Mabry's result.
