  (Talk presented at the 1992 ICTP summer workshop in high energy physics and
cosmology) The BRST cohomology ring for $(p,q)$ models coupled to gravity is
discussed. In addition to the generators of the ghost number zero ring, the
existence of a generator of ghost number $-1$ and its inverse is proven and
used to construct the entire ring. Some comments are made regarding the algebra
of the vector fields on the ring and the supersymmetric extension.
