  We show how the double cohomology of the String and Felder BRST charges
naturally leads to the ring structure of $c<1$ strings. The chiral ring is a
ring of polynomials in two variables modulo an equivalence relation of the form
$x^p \simeq y^{p+1}$ for the (p+1,p) model. We also study the states
corresponding to the edges of the conformal grid whose inclusion is crucial for
the closure of the ring. We introduce candidate operators that correspond to
the observables of the matrix models. Their existence is motivated by the
relation of one of the screening operators of the minimal model to the zero
momentum dilaton.
