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In the review article the influence of the Rashba spin-orbit coupling on thetwo-dimensional electrons and holes in a strong perpendicular magnetic field isdescribed in Landau gauge using the spinor-type two-component wave functionswith different numbers of the Landau quantization levels in different spinprojections, their difference being determined by the order of the chiralityterms. In this representation the two-particle integral operators such as theelectron and hole densities ${{\hat{\rho}}_{e}}(\vec{Q})$, and${{\hat{\rho}}_{h}}(\vec{Q})$ as well as the magnetoexciton creation andannihilation operators $\hat{\Psi}_{ex}^{\dagger}({{F}_{n}},\vec{k})$ and$\hat{\Psi}_{ex}^{{}}({{F}_{n}},\vec{k})$ in different combinations ${{F}_{n}}$of the electron and hole spinor states were introduced. On this base theHamiltonians of the Coulomb electron-electron and electron-radiationinteractions were deduced. The properties of the magnetoexcitons in theseconditions were discussed.

The influence of the Rashba spin-orbit coupling on the two-dimensional electron-hole system and magnetoexcitons