Within the framework of the method of formal dressing transformations, we construct a family of zero-curvature equations with discrete space variable for the case of the algebra gl(n, ℂ((λ^-1))). The equations obtained admit reduction with respect to the gauge group and, on the quotient, give rise to the nth order scalar difference equations that can be regarded as discrete analogs of KdV-equations. It is proved that the flows corresponding to different equations of the family commute.