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The influence of rotation on the structure and dynamics of sheared turbulence is investigated using a series of direct numerical simulations. Five cases are considered: turbulent shear flow without rotation, with moderate rotation, and with strong rotation, where the rotation configuration is either parallel or antiparallel. For moderate rotation rates an antiparallel configuration increases the growth of the turbulent kinetic energy, while the parallel case reduces the growth as compared to the nonrotating case. For strong rotation rates decay of the energy is observed, linear effects dominate the flow, and the vorticity probability density functions tend to become Gaussian. Visualizations of vorticity show that the inclination angle of the vortical structures depends on the rotation rate and orientation. Coherent vortex extraction, based on the orthogonal wavelet decomposition of vorticity, is applied to split the flow into coherent and incoherent parts. It was found that the coherent part preserves the vortical structures using only a few percent of the degrees of freedom. The incoherent part was found to be structureless and of mainly dissipative nature. With increasing rotation rates, the number of wavelet modes representing the coherent vortices decreases, indicating an increased coherency of the flow. Restarting the direct numerical simulation with the filtered fields confirms that the coherent component preserves the temporal dynamics of the total flow, while the incoherent component is of dissipative nature.