  Since the invention of space-time coding numerous algebraic methods have been
applied in code design.
  In particular algebraic number theory and central simple algebras have been
on the forefront of the research.
  In this paper we are turning the table and asking whether information theory
can be used as a tool in algebra. We will first derive some corollaries from
diversity-multiplexing gain (DMT) bounds by Zheng and Tse and later show how
these results can be used to analyze the unit group of orders of certain
division algebras. The authors do not claim that the algebraic results are new,
but we do find that this interesting relation between algebra and information
theory is quite surprising and worth pointing out.
