  Using bicomplex formalism we construct generalizations of Fordy-Kulish
systems of matrix nonlinear Schroedinger equations on two-dimensional
space-time in two respects. Firstly, we obtain corresponding equations in three
space-time dimensions. Secondly, a Moyal deformation is applied to the
space-time coordinates and the ordinary product of functions replaced by the
Moyal product in a suitable way. Both generalizations preserve the existence of
an infinite set of conservation laws.
