A search is presented for the production of a single top quark vialeft-handed flavour-changing neutralcurrent (FCNC) interactions of a topquark, a gluon and an up or charm quark. Two production processes areconsidered: u + g -> t and c + g -> t. The analysis is based onproton-proton collision data taken at a centre-of-mass energy of 13 TeVwith the ATLAS detector at the LHC. The data set corresponds to anintegrated luminosity of 139 fb(-1). Events with exactly one electron ormuon, exactly one b-tagged jet and missing transverse momentum areselected, resembling the decay products of a singly produced top quark.Neural networks based on kinematic variables differentiate betweenevents from the two signal processes and events from backgroundprocesses. The measured data are consistent with the background-onlyhypothesis, and limits are set on the production cross-sections of thesignal processes: sigma(u + g -> t) x B(t -> Wb) x B(W -> l nu) < 3.0 pband sigma(c + g -> t) xB(t -> Wb) xB(W -> l nu) < 4.7pb at the 95\%confidence level, with B(W -> l nu) = 0.325 being the sum of branchingratios of all three leptonic decay modes of the W boson. Based on theframework of an effective field theory, the cross-section limits aretranslated into limits on the strengths of the tug and tcg couplingsoccurring in the theory: vertical bar C-uG(ut)vertical bar Lambda(2) <0.057 TeV-2 and vertical bar C-uG(ct)vertical bar Lambda(2) < 0.14TeV-2. These bounds correspond to limits on the branching ratios ofFCNC-induced top-quark decays: B(t -> u + g) < 0.61 x 10(-4) and B(t ->c + g) < 3.7 x 10(-4).