  The influence of the interaction between electrons on the Aharonov-Bohm
effect is investigated in the framework of the Hubbard model. The repulsion
between electrons associated with strong correlation is compared with the case
of attraction such as $U$-center pairing. The most interesting case, when two
electrons are located on a ring, is investigated in detail using the Bethe
ansatz method and by exact numerical diagonalization of the Hubbard
hamiltonian. It is shown that the quasi half quantum flux periodicity occurs
for any nonzero values of $U$. For large number of sites, or strong U, the
quasi periodicity becomes an exact half quantum flux periodicity. However the
character of the state created on the ring is different in both cases. In the
case of $U$-center pairing the electrons are bound in pairs located on the same
site. For strong correlations(large positive $ U$) the electrons tend to be far
from each other as possible. We show by numerical solution of Bethe ansaz
equations that for three electrons the flux periodicity of the ground state
energy is equal to 1/3. The one third periodicity may occur even for small
values of the ratio $U/t$, for the very dilute system. It is shown analytically
using the Bethe ansaz equations for $N$ electrons, that for dilute systems with
arbitrary value of the Hubbard repulsion $U$,
