  The Moyal momentum algebra is, once again, used to discuss some important
aspects of NC integrable models and 2d conformal field theories. Among the
results presented, we setup algebraic structures and makes useful convention
notations leading to extract non trivial properties of the Moyal momentum
algebra. We study also the Lax pair building mechanism for particular examples
namely, the noncommutative KdV and Burgers systems. We show in a crucial step
that these two systems are mapped to each others through a crucial mapping.
This makes a strong constraint on the NC Burgers system which corresponds to
linearizing its associated differential equation. From the conformal field
theory point of view, this constraint equation is nothing but the analogue of
the conservation law of the conformal current. We believe that this mapping
might help to bring new insights towards understanding the integrability of
noncommutative 2d-systems.
