Left-right single-spin asymmetries are measured in inclusive deep inelastic scattering at HERMES, with the goal of searching for a 2-photon exchange signal in the range 0.004 < x < 0.9, 0.1 < g^ < 20 GeV^. In two separate regions, for Q^ > 1 GeV^ and Q^ < 1 GeV^, and for both electron and positron beams, the asymmetries are found to be consistent with zero showing that within the uncertainties no signal is detected.