Final results are presented from the inclusive measurement of deep-inelastic polarised-muon scattering on longitudinally polarised deuterons using a (LiD)-Li-6 target. The data were taken at 160 GeV beam energy and the results are shown for the kinematic range 1 (GeV/c)(2) < Q(2) < 100 (GeV/c)(2) in photon virtuality, 0.004 < x < 0.7 in the Bjorken scaling variable and W > 4GeV/c(2) in the mass of the hadronic final state. The deuteron double-spin asymmetry A(1)(d) and the deuteron longitudinal-spin structure function g(1)(d) are presented in bins of x and Q(2). Towards lowest accessible values of x, g(1)(d) decreases and becomes consistent with zero within uncertainties. The presented final g(1)(p) values together with the recently published final g(1)(p) values of COMPASS are used to again evaluate the Bjorken sum rule and perform the QCD fit to the g(1) world data at next-to-leading order of the strong coupling constant. In both cases, changes in central values of the resulting numbers are well within statistical uncertainties. The flavour singlet axial charge a(0), which is identified in the MS renormalisation scheme with the total contribution of quark helicities to the nucleon spin, is extracted at next-to-leading order accuracy from only the COMPASS deuteron data: a(0)(Q(2) = 3 (GeV/c)(2)) = 0.32 +/- 0.02(stat) +/- 0.04(syst) +/- 0.05(evol). Together with the recent results on the proton spin structure function g(1)(p), the results on g(1)(d) constitute the COMPASS legacy on the measurements of g(1) through inclusive spin-dependent deep inelastic scattering. (C) 2017 The Author(s). Published by Elsevier B.V.