  We investigate the interplay of ferroelectricity and quantum electron
transport at the nanoscale in the regime of Coulomb blockade. Ferroelectric
polarization in this case is no longer the external parameter but should be
self-consistently calculated along with electron hopping probabilities leading
to new physical transport phenomena studying in this paper. These phenomena
appear mostly due to effective screening of a grain electric field by
ferroelectric environment rather than due to polarization dependent tunneling
probabilities. At small bias voltages polarization can be switched by a single
excess electron in the grain. In this case transport properties of SET exhibit
the instability (memory effect).
