  This paper aims at the following results: \begin{enumerate} \item The class
of all $*$-regular rings forms a variety. \item A subdirectly irreducible
  $*$-regular ring $R$
  is faithfully representable
  (i.e. isomorphic to a subring of an endomorphisms ring of
  vector spaces, where the involution is given by
  adjunction with respect to a scalar product on the vector space) if so is its
ortholattice of projections. \end{enumerate} This is a short version of the
second author's PhD thesis.
