  Phase effects on the conductance of a double-dot system in a ring structure
threaded by a magnetic flux are studied. The Aharonov-Bohm effect combined with
the dot many-body charging effects determine the phases of the currents going
through each arm of the ring. The cases for zero magnetic flux or half a
quantum of flux are discussed in detail. It is shown that, depending upon the
magnetic flux and the state of charge of the dots, controlled by gate
potentials, the dephasing of the upper and lower arm current gives rise to a
$S=1/2$ or S=1 Kondo regime. We also show that even in the absence of a
magnetic flux there can be a circulating current in the ring, depending on the
system parameters.
