  We investigate the phase diagram of a generalized spin-1/2 quantum
antiferromagnet on a ladder with rung, leg, diagonal, and ring-exchange
interactions. We consider the exactly soluble models associated with the
problem, obtain the exact ground states which exist for certain parameter
regimes, and apply a variety of perturbative techniques in the regime of strong
ring-exchange coupling. By combining these approaches with considerations
related to the discrete Z_4 symmetry of the model, we present the complete
phase diagram.
