A systematic theoretical approach is developed to study the electronic and transport properties of a twodimensional electron gas (2DEG) in the presence of spin-orbit interactions induced by the Rashba effect. The standard random-phase approximation is employed to calculate the screening length caused by electron-electron interaction in different transition channels. The quantum and transport mobilities in different spin branches are evaluated using the momentum-balance equation derived from the Boltzmann equation,in which the electron interactions with both the remote and background impurities are taken into account in an InAlAs/InGaAs heterojunction at low-temperatures.