  We address the dynamics induced by collective atomic recoil in a
Bose-Einstein condensate in presence of radiation losses and atomic
decoherence. In particular, we focus on the linear regime of the lasing
mechanism, and analyze the effects of losses and decoherence on the generation
of entanglement. The dynamics is that of three bosons, two atomic modes
interacting with a single-mode radiation field, coupled with a bath of
oscillators. The resulting three-mode dissipative Master equation is solved
analytically in terms of the Wigner function. We examine in details the two
complementary limits of {\em high-Q cavity} and {\em bad-cavity}, the latter
corresponding to the so-called superradiant regime, both in the quasi-classical
and quantum regimes. We found that three-mode entanglement as well as two-mode
atom-atom and atom-radiation entanglement is generally robust against losses
and decoherence,thus making the present system a good candidate for the
experimental observation of entanglement in condensate systems. In particular,
steady-state entanglement may be obtained both between atoms with opposite
momenta and between atoms and photons.
