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In the review article the influence of the Rashba spin-orbit coupling on the two-dimensional electrons and holes in a strong perpendicular magnetic field is described in Landau gauge using the spinor-type two-component wave functions with different numbers of the Landau quantization levels in different spin projections, their difference being determined by the order of the chirality terms. In this representation the two-particle integral operators such as the electron and hole densities ${{\hat{\rho}}_{e}}(\vec{Q})$, and ${{\hat{\rho}}_{h}}(\vec{Q})$ as well as the magnetoexciton creation and annihilation 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 the Hamiltonians of the Coulomb electron-electron and electron-radiation interactions were deduced. The properties of the magnetoexcitons in these conditions were discussed.

The Influence of the Rashba Spin-Orbit Coupling on the Two-Dimensional Electron–Hole System and Magnetoexcitons