  The processes of the single W-production in hadron-hadron collisions are
suggested for investigation of the nucleon spin. An approach is proposed for
the determination of quark spin densities at low x. The lowest order
electroweak radiative corrections to the observable quantities are calculated.
The numerical calculations of the cross sections and the single spin
asymmetries taking into consideration the electroweak corrections at RHIC
energies have been made.
