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 GeV2 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 GeV2 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 d sigma/dQ(2) with R = 1 for Q(2) > 500 GeV2: 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 a good agreement with the running of alpha(s) as predicted by QCD. (C) 2007 Elsevier B.V. All rights reserved.