Using bicomplex formalism we construct generalizations of Fordy-Kulish syst
ems of matrix nonlinear Schrodinger 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-tim
e coordinates and the ordinary product of functions replaced by the Moyal p
roduct in a suitable way. Both generalizations preserve the existence of an
infinite set of conservation laws.