  Differential inclusive-jet cross sections have been measured for different
jet radii in neutral current deep inelastic ep scattering for boson
virtualities Q^2 > 125 GeV^2 with the ZEUS detector at HERA using an integrated
luminosity of 81.7 pb^-1. Jets were identified in the Breit frame using the k_T
cluster algorithm in the longitudinally inclusive mode for different values of
the jet radius R. Differential cross sections are presented as functions of Q^2
and the jet transverse energy, E_T,B^jet. The dependence on R of the
inclusive-jet cross section has been measured for Q^2 > 125 and 500 GeV^2 and
found to be linear with R in the range studied. Next-to-leading-order QCD
calculations give a good description of the measurements for 0.5 <= R <= 1. A
value of alpha_s(M_Z) has been extracted from the measurements of the
inclusive-jet cross-section dsigma/dQ^2 with R=1 for Q^2 > 500 GeV^2:
alpha_s(M_Z) = 0.1207 +- 0.0014 (stat.) -0.0033 +0.0035 (exp.) -0.0023 +0.0022
(th.). The variation of alpha_s with E_T,B^jet is in good agreement with the
running of alpha_s as predicted by QCD.
