We study the Kondo screening effect generated by a single-electron transist
or or quantum dot embedded in a small metallic ring. When the ring circumfe
rence L becomes comparable to the fundamental length scale xi (0)(K) = h(up
silonF)/T-K(0) associated with the bulk Kondo temperature, the Kondo resona
nce is strongly affected, depending on the total number of electrons (mod4)
and magnetic flux threading the ring. The resulting Kondo-assisted persist
ent currents are also calculated in both Kondo and mixed-valence regimes, a
nd the maximum values are found in the crossover region.