Some natural additive decompositions of elements in bimodules

We consider a small category naturally associated with any fixed R-S-bimodule MSR. The class of objects of this category is the underlying set M of MSR. Some additive decompositions of the elements of the bimodule MSR appear naturally. They are the analog of the usual decompositions of the identity 1R of a ring R as sums of pairwise orthogonal idempotents. We extend results by Campanini, El-Deken and Facchini from the category Morph(Mod-R) of all morphisms in the category Mod-R to arbitrary bimodules MSR.