  In this paper we examine thoroughly the single (anti-)top quark production
associated with a lightest neutralino at the possible CERN Large Hadron
Electron Collider (LHeC). We calculate the full next-to-leading order (NLO) QCD
corrections to the process including all the nonresonant diagrams and do not
assume the production and decay factorization for the possible resonant top
squarks in the R-parity violating minimal supersymmetric standard model with 19
unrelated parameters. We investigate numerically the effects of the relevant
supersymmetry (SUSY) parameters on the cross section, and present the
transverse momentum distributions of final (anti-)top quark at both the
leading-order (LO) and the QCD NLO. We find that the NLO QCD corrections
enhance the LO cross sections in most chosen parameter space, and the NLO QCD
impacts on the transverse momentum distributions of the final (anti-)top quark
might be resolvable in some cases. We conclude that even with recently known
experimental constraints the on SUSY parameters, the production rate could
still achieve notable value in the admissible parameter space.
