  We develop the symbolic representation method to derive the hierarchies of
$(2+1)$-dimensional integrable equations from the scalar Lax operators and to
study their properties globally. The method applies to both commutative and
noncommutative cases in the sense that the dependent variable takes its values
in ${\mathbb C}$ or a noncommutative associative algebra. We prove that these
hierarchies are indeed quasi-local in the commutative case as conjectured by
Mikhailov and Yamilov in 1998. We propose a ring extension based on the
symbolic representation. As examples, we give noncommutative versions of KP,
mKP and Boussinesq equations.
