  A stationary random sequence admits under some assumptions a representation
as the sum of two others: one of them is a martingale difference sequence, and
another is a so-called coboundary. Such a representation can be used for
proving some limit theorems by means of the martingale approximation. A
multivariate version of such a decomposition is presented in the paper for a
class of random fields generated by several commuting non-invertible
probability preserving transformations. In this representation summands of
mixed type appear which behave with respect to some groupof directions of the
parameter space as reversed multiparameter martingale differences (in the sense
of one of several known definitions) while they look as coboundaries relative
to the other directions. Applications to limit theorems will be published
elsewhere.
