  The isotropic S=1/2 antiferromagnetic spin ladder with additional four-spin
ring exchange is studied perturbatively in the strong coupling regime with the
help of cluster expansion technique, and by means of bosonization in the weak
coupling limit. It is found that a sufficiently large strength of ring exchange
leads to a second-order phase transition, and the shape of the boundary in the
vicinity of the known exact transition point is obtained. The critical exponent
for the gap is found to be $\eta\simeq1$, in agreement both with exact results
available for the dimer line and with the bosonization analysis. The phase
emerging for high values of the ring exchange is argued to be gapped and
spontaneously dimerized. The results for the transition line from strong
coupling and from weak coupling match with each other naturally.
