On two sequences of sets of mappings of abstract sets into a Dedekind ring

This paper establishes some interrelations between a finite sequence of sets of mappings of an abstract set S into complete residue systems of pairwise relatively prime elements of any Dedekind ring and the corresponding sequence of sets of mappings of the set S into the complete residue system corresponding to the product of these elements. A relationship is revealed between the established interrelation and Lang’s theorem on isomorphic factor rings. A string model is presented that is an interpretation of structures investigated in the cases of the ring of integers and a one-element set S. It is shown that the results obtained can be used for computing the number of combinatorial objects defined in terms of finite residue rings.