The production of $eta$ mesons in the reactions $ppto ppeta$ and $pnto pneta $ at threshold-near energies is analyzed within a covariant effective meson-nucleon theory. The description of cross section and angular distributions of the available data in this kinematical region in the $pp$ channel is accomplished by including meson currents and nucleon currents with the resonances $S_{11}(1650)$, $P_{11}(1710)$ and $P_{13}(1720)$. Predictions for the $pn$ channel are given. The di-electron production from subsequent $eta$ Dalitz decay $eta to gamma gamma^* togamma e^+e^-$ is also calculated and numerical results are presented for intermediate energy and kinematics of possible experiments with HADES, CLAS and KEK-PS.
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