  In two-dimensional noncommutive space for the case of both position -
position and momentum - momentum noncommuting, the consistent deformed bosonic
algebra at the non-perturbation level described by the deformed annihilation
and creation operators is investigated. A general relation between
noncommutative parameters is fixed from the consistency of the deformed
Heisenberg - Weyl algebra with the deformed bosonic algebra. A Fock space is
found, in which all calculations can be similarly developed as if in
commutative space and all effects of spatial noncommutativity are simply
represented by parameters.
