Inclusive jet production is studied in neutral current deep-inelastic positron-proton scattering at large four momentum transfer squared Q^2>150 GeV^2 with the H1 detector at HERA. The measurements are found to be well described by calculations at next-to-leading order in perturbative QCD. The running of the strong coupling is demonstrated and the value of alpha_s(M_Z) is determined.
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