  We present a powerful method to generate various equations which possess the
Lax representations on noncommutative (1+1) and (1+2)-dimensional spaces. The
generated equations contain noncommutative integrable equations obtained by
using the bicomplex method and by reductions of the noncommutative
(anti-)self-dual Yang-Mills equation. This suggests that the noncommutative Lax
equations would be integrable and be derived from reductions of the
noncommutative (anti-)self-dual Yang-Mills equation, which implies the
noncommutative version of Richard Ward conjecture. The integrability and the
relation to string theories are also discussed.
