Sums of order bounded disjointness preserving linear operators

Necessary and sufficient conditions are found under which the sum of $N$ order bounded disjointness preserving operators is $n$-disjoint with $n$ and $N$ naturals. It is shown that the decomposition of an order bounded $n$-disjoint operator into a sum of disjointness preserving operators is unique up to “Boolean permutation”, the meaning of which is clarified in the course of the presentation.