  We demonstrate that in strong quantum limit the thermoelectric Peltier effect
could define the longitudinal resistivity of dissipationless two-dimensional
electron(hole) gas. The current results in heating(cooling) at first(second)
Hall bar sample contact due to Peltier effect. At small current the contacts
temperatures are different, the temperature gradient is linear on current. The
voltage swing downstream the current is proportional to Peltier effect induced
thermopower. As a result, nonzero longitudinal resistivity is measured in
experiment. The above effect could exist in 3D case.
